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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CSSE</journal-id>
<journal-id journal-id-type="nlm-ta">CSSE</journal-id>
<journal-id journal-id-type="publisher-id">CSSE</journal-id>
<journal-title-group>
<journal-title>Computer Systems Science &#x0026; Engineering</journal-title>
</journal-title-group><issn pub-type="ppub">0267-6192</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">14929</article-id>
<article-id pub-id-type="doi">10.32604/csse.2021.014929</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Atrocious Impinging of COVID-19 Pandemic on Software Development Industries</article-title><alt-title alt-title-type="left-running-head">Atrocious Impinging of COVID-19 Pandemic on Software Development Industries</alt-title><alt-title alt-title-type="right-running-head">Atrocious Impinging of COVID-19 Pandemic on Software Development Industries</alt-title>
</title-group>
<contrib-group content-type="authors">
<contrib id="author-1" contrib-type="author">
<name name-style="western">
<surname>Alhakami</surname>
<given-names>Wajdi</given-names>
</name>
<xref ref-type="aff" rid="aff-1">1</xref>
</contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western">
<surname>Binmahfoudh</surname>
<given-names>Ahmed</given-names>
</name>
<xref ref-type="aff" rid="aff-2">2</xref>
</contrib>
<contrib id="author-3" contrib-type="author">
<name name-style="western">
<surname>Baz</surname>
<given-names>Abdullah</given-names>
</name>
<xref ref-type="aff" rid="aff-3">3</xref>
</contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western">
<surname>Alhakami</surname>
<given-names>Hosam</given-names>
</name>
<xref ref-type="aff" rid="aff-4">4</xref>
</contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western">
<surname>Ansari</surname>
<given-names>Md Tarique Jamal</given-names>
</name>
<xref ref-type="aff" rid="aff-5">5</xref>
</contrib>
<contrib id="author-6" contrib-type="author" corresp="yes">
<name name-style="western">
<surname>Khan</surname>
<given-names>Raees Ahmad</given-names>
</name>
<xref ref-type="aff" rid="aff-5">5</xref>
<email>khanraees@yahoo.com</email>
</contrib>
<aff id="aff-1">
<label>1</label><institution>Department of Information Technology, College of Computers and Information Technology, Taif University</institution>, <addr-line>Taif, 21944</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2">
<label>2</label><institution>Department of Computer Engineering, College of Computers and Information Technology, Taif University</institution>, <addr-line>Taif, 21944</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3">
<label>3</label><institution>Department of Computer Engineering, College of Computer and Information Systems, Umm Al-Qura University</institution>, <addr-line>Makkah, 21955</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4">
<label>4</label><institution>Department of Computer Science, College of Computer and Information Systems, Umm Al-Qura University</institution>, <addr-line>Makkah, 21955</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-5">
<label>5</label><institution>Department of Information Technology, Babasaheb Bhimrao Ambedkar University</institution>, <addr-line>Lucknow, 226025</addr-line>, <country>India</country></aff>
</contrib-group><author-notes><corresp id="cor1">&#x002A;Corresponding Author: Raees Ahmad Khan. Email: 
<email>khanraees@yahoo.com</email></corresp></author-notes>
<pub-date pub-type="epub" date-type="pub" iso-8601-date="2021-11-30">
<day>30</day>
<month>11</month>
<year iso-8601-date="2021">2021</year>
</pub-date>
<volume>36</volume>
<issue>2</issue>
<fpage>323</fpage>
<lpage>338</lpage>
<history>
<date date-type="received">
<day>28</day>
<month>10</month>
<year iso-8601-date="2020">2020</year>
</date>
<date date-type="accepted">
<day>17</day>
<month>11</month>
<year iso-8601-date="2020">2020</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2021 Alhakami et al.</copyright-statement>
<copyright-year>2021</copyright-year>
<copyright-holder>Alhakami et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CSSE_14929.pdf"></self-uri>
<abstract>
<p>COVID-19 is the contagious disease transmitted by Coronavirus. The majority of people diagnosed with COVID-19 may suffer from moderate-to- severe respiratory illnesses and stabilize without preferential treatment. Those who are most likely to experience significant infections include the elderly as well as people with a history of significant medical issues including heart disease, diabetes, or chronic breathing problems. The novel Coronavirus has affected not only the physical and mental health of the people but also had adverse impact on their emotional well-being. For months on end now, due to constant monitoring and containment measures to combat COVID-19, people have been forced to live in isolation and maintain the norms of social distancing with no community interactions. Social ties, experiences, and partnerships are not only integral part of work life but also form the basis of human evolvement. However, COVID-19 brought all such communication to a grinding halt. Digital interactions have failed to support the fervor that one enjoys in face-to-face meets. The COVID-19 disease outbreak has triggered dramatic changes in many sectors, and the main among them is the software industry. This paper aims at assessing COVID-19&#x2019;s impact on Software Industries. The impact of the COVID-19 disease outbreak has been measured on the basis of some predefined criteria for the demand of different software applications in the software industry. For the stated analysis, we used an approach that involves the application of the integrated Fuzzy ANP and TOPSIS strategies for the assessment of the impact of COVID-19 on the software industry. Findings of this research study indicate that Government administration based software applications were severely affected, and these applications have been the major apprehensions in the wake of the pandemic&#x2019;s outbreak. Undoubtedly, COVID-19 has had a considerable impact on software industry, yet the damage is not irretrievable and the world&#x2019;s societies can emerge out of this setback through concerted efforts in all facets of life.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Coronavirus</kwd>
<kwd>software industry</kwd>
<kwd>safety</kwd>
<kwd>COVID-19 monitoring</kwd>
<kwd>fuzzy ANP-TOPSIS</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Humans all around the globe have been living in a state of perpetual fear ever since COVID-19 disease was declared a global pandemic. This pandemic has had a massive and unprecedented impact on the lives of millions across the globe, triggering feelings of isolation, confusion, frustration and hopelessness. This apprehension coupled with the economic meltdown is also because many people are experiencing severe symptoms of depression. The spread of COVID-19 is a significant threat to the society both as a result of the possibility that people may suffer from financial distress and due to its unknown mental stress. The pandemic is assumed to be this century&#x2019;s most fatal world health calamity as well as the biggest obstacle being faced by the humanity since the Second World War [<xref ref-type="bibr" rid="ref-1">1</xref>]. The World Health Organization (WHO) declared COVID-19 a Public Health Emergency of International Concern (PHEIC) on January 31, 2020. This meant that the disease could result in significant harm to several countries and required an immediate, collaborative worldwide response [<xref ref-type="bibr" rid="ref-2">2</xref>]. Further to the announcement, the WHO confirmed the outbreak of COVID-19 as a &#x201C;pandemic public health menace&#x201D; on 11 March 2020. COVID-19 cases have grown alarmingly in several countries across the globe [<xref ref-type="bibr" rid="ref-3">3</xref>].</p>
<p>Premature findings demonstrate that marginalized people suffer significantly from the financial and health consequences of the COVID-19. The absence of face-to-face interactions and virtual confinement due to shutdowns has led to anxiety, depression, psychiatric illnesses, impacting the health of individuals as well as the social system as a whole [<xref ref-type="bibr" rid="ref-4">4</xref>]. The COVID-19 disease outbreak is much more than just a health emergency; at its core it affects the economy and the society. Although the effects of this pandemic may vary significantly from country to country, economic inequality and imbalances would most probably increase on a worldwide scale. The global spread of COVID-19 has also produced several privacy, data safety, and security concerns for the software industry [<xref ref-type="bibr" rid="ref-5">5</xref>&#x2013;<xref ref-type="bibr" rid="ref-7">7</xref>].</p>
<p>The COVID-19 disease outbreak has affected the markets and different industries around the world. Software industry has registered a substantial rise in demand for software applications. This rise can be directly attributed to COVID-19 disease outbreak, and its industrial consequences have attracted considerable attention from the academicians and researchers. Every human being goes through wellness and illness throughout their lifespan [<xref ref-type="bibr" rid="ref-8">8</xref>]. While illnesses are personal, the infection starts affecting the patients and family members first and then the entire social group. Gradually, the struggle of many individuals from illnesses over a period of time along with the synchronous replication of illnesses by interpersonal social layers, the socio-cultural consciousness of the illnesses, and the imbalances encountered in accessing healthcare services become the major crisis areas. These issues call for a societal standpoint. More specifically, in case of a pandemic, since many individuals are infected by the same contagion, they impact populations differently as against the classical illnesses. Pandemics are seen as dreadful phenomena in social histories [<xref ref-type="bibr" rid="ref-8">8</xref>&#x2013;<xref ref-type="bibr" rid="ref-10">10</xref>]. They are known to cause enormous panic among common people, compelling them to live in a state of fear and uncertainty. Pandemics disrupt life&#x2019;s natural process, and everyone has a specific experience of the disease outbreak. Therefore, health information begins to emerge that is passed on from one generation to another.</p>
<p>Hence, this research attempts to implement a hybrid method that uses the integration of fuzzy and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to calculate the effect of Coronavirus dispersion on numerous factors of software industry. Using the Multi-Criteria Decision Making (MCDM) approach, we selected different software industry&#x2019;s factors that were affected by COVID-19 pandemic on the basis of some specified criteria. MCDM is Operation Research&#x2019;s most significant component through which people can take their daily decisions in a nuanced manner. Several researchers are modeling many of the MCDM instruments. All these MCDM ideas are built on decision-making behavioral issues. Individuals pick the best alternative options in the MCDM procedure with regard to certain factors. These MCDM techniques have also been used to solve different decision making issues due to COVID-19 pandemic [<xref ref-type="bibr" rid="ref-11">11</xref>&#x2013;<xref ref-type="bibr" rid="ref-14">14</xref>]. Thus, to obtain accurate and conclusive results, the present study also employs the MCDM technique for the intended estimation.</p>
<p>The rest of this paper has been arranged as follows: Section 2 discusses the impact of novel COVID-19 on software industry. Section 3 deliberates upon the materials and methods used in this research study. Section 4 presents the empirical analysis and findings of the proposed study. The results&#x2019; sensitivity analysis and comparison with different approaches are detailed in Section 5. Section 6 discusses the findings of this research study. Finally, Section 7 presents the conclusion.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>The Impact of COVID-19 on Software Industry</title>
<p>Pandemics have always damaging effect on industries at all levels. COVID-19 pandemic is not only a worldwide health emergency; it is also the biggest cause of economic upheavals across the globe now. As the world grapples with the crisis and works towards containing the spread of the virus, the policymakers should also plan for the next step. The next &#x201C;natural&#x201D; is not however. However, there is no definitive pattern or standard available to aid the decisions of the strategists. Moreover, the standard operating procedure in the case of preventive measures for Coronavirus like social distancing, wearing masks is not accessible to everyone. The modern reality is made of ambiguity, confusion and possibilities. Unfortunately, the pandemic has further underscored these debacles. In such a scenario, organizations have to be flexible and agile with robust mechanisms that can help them to adjust and survive. COVID-19 has had a significant impact on the software industry, affecting the supply of resources, interrupting the production chain of the consumer products, besides triggering inflation risk in goods. In a positive way, the interruption led to acceleration in the phenomenon of working remotely, like work-from-home is the new norm in most of the organizations now. In this process, the end-to-end chain has been tested and made risk-free. Moreover, limited or no travel in the recent months implied less vehicular pollution. Thus, decrease in carbon emissions may contribute to a renewed emphasis on sustainable growth.</p>
<p>The Coronavirus outbreak has pointed to revamped tech expenditure growth estimates in 2020. A survey&#x2019;s findings published on Statista Portal demonstrate the effect of COVID-19 pandemic on the consumer spending trend from May 2020. Though most customers foresee no adjustments in their tech spending, the majority of the respondents reported a decrease in spending than a rise in spending. This trend of decline in spending covers nearly all the industries [<xref ref-type="bibr" rid="ref-5">5</xref>]. The graphical representation of this study can be seen in <xref ref-type="fig" rid="fig-1">Fig. 1</xref>. Most software developers do have action plans; however, these plans do not completely resolve the rapidly evolving uncontrollable factors of an emergency such as COVID-19. Standard safety measures are structured to ensure operating efficiency following, among many other items, natural disasters, cyber-attacks and power failures. Normally, they do not take into consideration the common quarantines, prolonged university shutdowns and additional travel bans in the emergency situation for healthcare systems. Hence, the impact of the pandemic on the software industry has been detrimental in more ways than one.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Industry-wise impact of COVID-19 on software spending worldwide</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="fig-1.png"/>
</fig>
</sec>
<sec id="s3">
<label>3</label>
<title>Materials and Methods</title>
<sec id="s3_1">
<label>3.1</label>
<title>Criteria and Alternatives Selection</title>
<p>Review of the existing literature and experienced and professional questionnaire-based surveys were designed for conducting this research paper&#x2019;s empirical calculations. We analyzed approximately 30 publications to select those factors of the software industry that have been affected by the spread of COVID-19 pandemic. It is demonstrated in previous studies that each of the selected factors has somehow been influenced by Coronavirus. Therefore, we premised our literature search on the essential criteria for selecting the alternatives in this study. Since our target was the analysis of the impact on the software, academic experts play an important role in this research. Opinions of several academicians and researchers from trusted organizations were sought for selecting the most relevant factors required to conduct this research work. Around 43 valid responses of 60 experts and researchers have been collated to select the highly affected software industry factors by COVID-19 pandemic.</p>
<p>It is supposed that the impact of software industry is based on seven criteria- the (ICi), and is responsible for seven alternatives solutions (SAi). The seven main criteria are: Functionality (IC1), Reliability (IC2), Flexibility (IC3), Costs (IC4), R&#x0026;D (IC5), Concept Conflict (IC6) and Risks (IC7). Seven alternatives are: Non-profit (SA1), Government Administration (SA2), Healthcare (SA3), Education (SA4), Insurance (SA5), IT &#x0026; Security (SA6), and Financial (SA7). In the second stage of the current process, because of COVID-19 pandemic spread, the alternatives were chosen as impacted factors in the society. These factors were identified by reviewing of the existing relevant literature, and then selected by a panel of specialists. <xref ref-type="table" rid="table-1">Tab. 1</xref> explicates all the identified criteria for evaluating the impact of pandemic on software industry factors. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> shows the hierarchy representation of our decision problem.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Evaluation criteria for the impact of COVID-19 on software industry</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Criteria</th>
<th>Description</th>
<th>References</th>
</tr>
</thead>
<tbody><tr>
<td><italic>Functionality (IC1)</italic></td>
<td>The functionality of a software application shows how useful it is or how many functions it can perform. Marketing departments use the versatility of a software product to define service offerings, and encourage a customer to have a collection of capabilities. Functionality can be simple to use, or complex.</td>
<td>[<xref ref-type="bibr" rid="ref-10">10</xref>&#x2013;<xref ref-type="bibr" rid="ref-12">12</xref>]</td>
</tr>
<tr>
<td><italic>Reliability (IC2)</italic></td>
<td>Reliability is a characteristic of any software application that operates reliably as per its specified requirements. It must be considered when producing, purchasing or using a software product.</td>
<td>[<xref ref-type="bibr" rid="ref-15">15</xref>,<xref ref-type="bibr" rid="ref-16">16</xref>]</td>
</tr><tr>
<td><italic>Flexibility (IC3)</italic></td>
<td>A distinguishing characteristic of software application is the versatility of software designs, especially where methods of software development require the use of a variety of abilities.</td>
<td>[<xref ref-type="bibr" rid="ref-17">17</xref>,<xref ref-type="bibr" rid="ref-18">18</xref>]</td>
</tr><tr>
<td><italic>Costs (IC4)</italic></td>
<td>This includes expenses on the development of software applications, testing, distribution, and reporting.</td>
<td>[<xref ref-type="bibr" rid="ref-19">19</xref>,<xref ref-type="bibr" rid="ref-20">20</xref>]</td>
</tr><tr>
<td><italic>R&#x0026;D (IC5)</italic></td>
<td>Research and Development is more than anything else, an analysis that seeks to create something new &#x2013; A finding which would lead to a new software service or product, or one that would boost or strengthen an available product.</td>
<td>[<xref ref-type="bibr" rid="ref-21">21</xref>,<xref ref-type="bibr" rid="ref-22">22</xref>]</td>
</tr><tr>
<td><italic>Concept Conflict (IC6)</italic></td>
<td>An issue which occurs when two programmes cannot run simultaneously on the same machine. Levels of software development can lead to software designers competing in different positions. Concept conflict has varying consequences for early investors vs. many organizations.</td>
<td>[<xref ref-type="bibr" rid="ref-23">23</xref>,<xref ref-type="bibr" rid="ref-24">24</xref>]</td>
</tr>
<tr>
<td><italic>Risks (IC7)</italic></td>
<td>In software industry, risk can be described as the probability that the actual results of an event or investment would vary from the intended results or returns. Risk involves a possible loss of any or all of an initial investment.</td>
<td>[<xref ref-type="bibr" rid="ref-25">25</xref>,<xref ref-type="bibr" rid="ref-26">26</xref>]</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>ANP structure of the evaluation of the impact of COVID-19 on software industry</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="fig-2.png"/>
</fig>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Fuzzy ANP-TOPSIS Method</title>
<sec id="s3_2_1">
<label>3.2.1</label>
<title>Fuzzy ANP</title>
<p>ANP was initiated by Saaty. It reflects a common analytical hierarchy (AHP) method [<xref ref-type="bibr" rid="ref-11">11</xref>]. Although AHP is a system with a unidirectional structured AHP arrangement, it is the ANP that enables effective interconnections between the levels as well as attributes of decisions. The ANP recommendations strategy substitutes hierarchies through networks that do not simply reflect the associations among levels as low or high, superior or inferior, implicit or explicit [<xref ref-type="bibr" rid="ref-12">12</xref>]. For example in a structure, the meaning and value of alternatives not only determines the meaning of the parameters, but it also may affect the validity of the parameters [<xref ref-type="bibr" rid="ref-11">11</xref>]. Furthermore, a continuous top-to-bottom design is not appropriate for a complicated process. AHP is a robust system intended to deal with logical, sensible and unreasonable choices, with or without assurance for a variety of alternatives, if we take multi-objective, multi-criteria and multi-actor choices. AHP&#x2019;s fundamental principles are that it is capable of using its entire lower portion and the parameters or objects in each category in the functional ability of the upper portion or group of the structure [<xref ref-type="bibr" rid="ref-12">12</xref>]. Most policy challenges cannot be hierarchically structured since the association and reliance of higher-level entities on low-level elements are involved [<xref ref-type="bibr" rid="ref-11">11</xref>,<xref ref-type="bibr" rid="ref-13">13</xref>&#x2013;<xref ref-type="bibr" rid="ref-15">15</xref>]. Responses between clusters are possible through the structuring of a functional dependency problem. It is a feature of the network. Saaty [<xref ref-type="bibr" rid="ref-11">11</xref>] proposed the utilization of AHP to fix the alternatives or parameters as independent issues including the use of ANP to overcome the question of alternatives or parameters&#x2019; dependency. The main transformation among ANP and AHP is that the structural weight can be accomplished through the creation of a &#x201C;supermatrix&#x201D; in order to handle interdependencies among the decision rates and parameters [<xref ref-type="bibr" rid="ref-14">14</xref>,<xref ref-type="bibr" rid="ref-27">27</xref>&#x2013;<xref ref-type="bibr" rid="ref-29">29</xref>].</p>
</sec>
<sec id="s3_2_2">
<label>3.2.2</label>
<title>Fuzzy TOPSIS</title>
<p>TOPSIS is among the most successful MCDM approach currently and has performed successfully in many application domains. Hwang and Yoon [<xref ref-type="bibr" rid="ref-15">15</xref>] were the first to cite an approach to overcome MCDM problems. According to them, the basic concept of this approach was to rank the alternative at the shortest distance from the given positive range as the best or the ideal solution, and the one at the farthest distance, the worst solution. Subsequently, Chen [<xref ref-type="bibr" rid="ref-16">16</xref>] expanded the TOPSIS system into a floating setting by replacing the numerical linguistic ranking and weighting rates by using TFNs (triangular fuzzy numbers). After the system propositioned by Chen, a variety of approaches were suggested for the modifications of the Fuzzy TOPSIS. For this paper, we have used the decision making process that was carried out by Chen [<xref ref-type="bibr" rid="ref-16">16</xref>], Fuzzy TOPSIS system. This approach is very appropriate in the fuzzy setting, particularly for solving the ambiguities that arise due to decision making by a group. Within this system, linguistic methods are considered as the weights of specific parameters and qualitative parameters scores [<xref ref-type="bibr" rid="ref-18">18</xref>,<xref ref-type="bibr" rid="ref-19">19</xref>]. The step-by-step process for determining the weights of the selected factors/attributes as well as the priority ranking obtained with the help of Fuzzy ANP-TOPSIS is defined as given below:</p>
<p><bold><italic>Step 1:</italic></bold> The linguistic words were converted first into simple quantitative data, and subsequently into Triangular Fuzzy Numbers (TFNs). In this research analysis the TFNs are indicated as (t1, t2, t3), in which (t1 t2 &#x003D; t3) and (t1, t2, t3) the least, intermedium and maximum value parameters in the TFNs are indicated. Suppose that A is a deceptive number which could also be shown by <xref ref-type="disp-formula" rid="eqn-1">Eqs. (1)</xref> and <xref ref-type="disp-formula" rid="eqn-2">(2)</xref> and also in <xref ref-type="fig" rid="fig-3">Fig. 3</xref> [<xref ref-type="bibr" rid="ref-26">26</xref>].</p>
<p><disp-formula id="eqn-1">
<label>(1)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-1.png"/><tex-math id="tex-eqn-1"><![CDATA[$${{\rm \mu }_{\rm A}}{\rm \; (x) = \; F} \to {\rm [0,1]}$$]]></tex-math><mml:math id="mml-eqn-1" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x03BC;</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">A</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="normal">x</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>&#x003D;</mml:mo><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mo stretchy="false">&#x2192;</mml:mo><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-2">
<label>(2)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-2.png"/><tex-math id="tex-eqn-2"><![CDATA[$${\mu _{\rm A}}\left( {\rm x} \right) = \left\{ {\matrix{ {\displaystyle{{{\rm x} - {\rm t}1} \over {{\rm t}2 - {\rm t}1}},\quad {\rm t}1 \le {\rm x} \le {\rm t}2} \hfill \cr {\displaystyle{{{\rm t}3 - {\rm x}} \over {{\rm t}3 - {\rm t}2}},\quad {\rm t}2 \le {\rm x} \le {\rm t}3} \hfill \cr {0,\quad {\rm x} > t3\quad Otherwise} \hfill \cr } } \right.$$]]></tex-math><mml:math id="mml-eqn-2" display="block"><mml:mrow><mml:msub><mml:mi>&#x03BC;</mml:mi><mml:mrow><mml:mi mathvariant="normal">A</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable columnspacing="1em" rowspacing="4pt"><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="1em"></mml:mspace><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>3</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>3</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow><mml:mo>,</mml:mo><mml:mspace width="1em"></mml:mspace><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mspace width="1em"></mml:mspace><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mo>&#x003E;</mml:mo><mml:mi>t</mml:mi><mml:mn>3</mml:mn><mml:mspace width="1em"></mml:mspace><mml:mi>O</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>w</mml:mi><mml:mi>i</mml:mi><mml:mi>s</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow><mml:mo stretchy="true" symmetric="true" fence="true"></mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<fig id="fig-3">
<label>Figure 3</label>
<caption>
<title>Triangular fuzzy number</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="fig-3.png"/>
</fig>
<p>Firstly, 50 specialists took differing opinions. All such specialists come from IT firms and academia and have a range of production and testing backgrounds with each set of characteristics and associated data. In a digital conference setting the specialists were asked to gather and evaluate their viewpoints and to be aware of the spectrum of qualities according to the various nationalities and standards.</p>
<p>With the appropriate support of the information recorded, authors from this study derived the network architecture. Various software industries were evaluated by the architecture to determine the weights of the properties of the effect of COVID-19. The specialists expressed their opinion by qualities that influence one another in a measurable way, with the help of a predefined scale which can be seen in <xref ref-type="table" rid="table-2">Tab. 2</xref>.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Scale of triangular fuzzy numbers</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Numerical Values</th><th colspan="2">Triangular Fuzzy Numbers</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>Equally significant</td>
<td>(1, 1, 1)</td>
</tr>
<tr>
<td>3</td>
<td>Weakly significant</td>
<td>(2, 3, 4)</td>
</tr>
<tr>
<td>5</td>
<td>Fairly significant</td>
<td>(4, 5, 6)</td>
</tr>
<tr>
<td>7</td>
<td>Strongly significant</td>
<td>(6, 7, 8)</td>
</tr>
<tr>
<td>9</td>
<td>Absolutely significant</td>
<td>(9, 9, 9)</td>
</tr>
<tr>
<td>2<break/>4<break/>6<break/>8</td>
<td>Intermittent values between two adjacent scales</td>
<td>(1, 2, 3)<break/>(3, 4, 5)<break/>(5, 6, 7)<break/>(7, 8, 9)</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Triangular fuzzy number (TFN) is constructed from precise numerical process variables using <xref ref-type="disp-formula" rid="eqn-3">Eqs. (3)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-6">(6)</xref> (t1ij, t2ij, t3ij), where t1ij mean lower level, t2ij means average level, and t3ij means maximum level. Triangular fuzzy number is produced from t2ij. The word TFN [&#x03B7;ij], from the other hand, is as follows:</p>
<p><disp-formula id="eqn-3">
<label>(3)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-3.png"/><tex-math id="tex-eqn-3"><![CDATA[$${\rm \; }{\eta _{{\rm ij}}} = {\rm \; }\left( {{\rm t}{1_{{\rm ij}}},{\rm \; t}{2_{{\rm ij}}},{\rm \; t}{3_{{\rm ij}}}} \right)$$]]></tex-math><mml:math id="mml-eqn-3" display="block"><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-24"><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-24.png"/><tex-math id="tex-eqn-24"><![CDATA[$${\rm where},{\rm \; \; \; \; \; \; \; t}{1_{{\rm ij}}} \le {\rm t}{2_{{\rm ij}}} \le {\rm t}{3_{{\rm ij}}}$$]]></tex-math><mml:math id="mml-eqn-24" display="block"><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2264;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-4">
<label>(4)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-4.png"/><tex-math id="tex-eqn-4"><![CDATA[$${\rm t}{1_{{\rm ij}}} = {\rm \; min}\left( {{{\rm J}_{{\rm ijd}}}} \right)$$]]></tex-math><mml:math id="mml-eqn-4" display="block"><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">J</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-5">
<label>(5)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-5.png"/><tex-math id="tex-eqn-5"><![CDATA[$${\rm t}{2_{{\rm ij}}} = {\left( {{{\rm J}_{{\rm ij}1}},{{\rm J}_{{\rm ij}2}},{{\rm J}_{{\rm ij}3}}} \right)^{{1 \over {\rm x}}}}$$]]></tex-math><mml:math id="mml-eqn-5" display="block"><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">J</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">J</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">J</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mrow></mml:msup></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-6">
<label>(6)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-6.png"/><tex-math id="tex-eqn-6"><![CDATA[$${\rm and\ t}{3_{{\rm ij}}} = {\rm \; max}\left( {{{\rm J}_{{\rm ijd}}}} \right)$$]]></tex-math><mml:math id="mml-eqn-6" display="block"><mml:mrow><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">n</mml:mi><mml:mi mathvariant="normal">d</mml:mi><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">J</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi><mml:mi mathvariant="normal">d</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>Jijk explains the relative influence of the variables on two variables, as the specialists have determined, described in accordance with the above equations. The term I and j signify a couple of characteristics that specialists decide in this situation. The TFN is determined in accordance with the geometrical mean of the judgment of the domain specialists for a precise reference. <xref ref-type="disp-formula" rid="eqn-7">Eqs. (7)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-9">(9)</xref> consequently enables TFN variables to be combined. There were two TFNs: A1 and A2; A1 &#x003D; (t11, t21, t31) and A2 &#x003D; (t12, t22, t32). They are subject to the following operational standards:</p>
<p><disp-formula id="eqn-7">
<label>(7)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-7.png"/><tex-math id="tex-eqn-7"><![CDATA[$$\left( {{\rm t}{1_1},{\rm \; t}{2_1},{\rm \; t}{3_1}} \right) + {\rm \; }\left( {{\rm t}{1_2},{\rm \; t}{2_2},{\rm \; t}{3_2}} \right) = {\rm \; }\left( {{\rm t}{1_1} + {\rm t}{1_2},{\rm \; \; t}{2_1} + {\rm t}{2_2},{\rm \; t}{3_1} + {\rm t}{3_2}} \right)$$]]></tex-math><mml:math id="mml-eqn-7" display="block"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x002B;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>&#x002B;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>&#x002B;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>&#x002B;</mml:mo><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-8">
<label>(8)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-8.png"/><tex-math id="tex-eqn-8"><![CDATA[$$\left( {{\rm t}{1_1},{\rm \; t}{2_1},{\rm \; t}{3_1}} \right) \times \left( {{\rm t}{1_2},{\rm \; t}{2_2},{\rm \; t}{3_2}} \right) = {\rm \; }\left( {{\rm t}{1_1}{\rm *t}{1_2},{\rm \; \; t}{2_1}{\rm *t}{2_2},{\rm \; t}{3_1}{\rm *t}{3_2}} \right)$$]]></tex-math><mml:math id="mml-eqn-8" display="block"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x00D7;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo>&#x2217;</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-9">
<label>(9)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-9.png"/><tex-math id="tex-eqn-9"><![CDATA[$${\left( {{\rm t}{1_1},{\rm \; t}{2_1},{\rm \; t}{3_1}} \right)^{ - 1}} = \left( {\displaystyle{1 \over {{\rm t}{3_1}}},\displaystyle{1 \over {{\rm t}{2_1}}},\displaystyle{1 \over {{\rm t}{1_1}}}} \right)$$]]></tex-math><mml:math id="mml-eqn-9" display="block"><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>,</mml:mo><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>,</mml:mo><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:mstyle></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><bold><italic>Step 2:</italic></bold> With the support of input from domain specialists, a matrix for a pair-wise comparison is constructed. Assessment of the Consistency Index (CI) is conducted employing <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref> formula according to following:</p>
<p><disp-formula id="eqn-10">
<label>(10)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-10.png"/><tex-math id="tex-eqn-10"><![CDATA[$${\rm CI\; } = {\rm \; }\left( {{{\rm \gamma }_{{\rm max}}} - {\rm c}} \right)/\left( {{\rm c} - 1} \right)$$]]></tex-math><mml:math id="mml-eqn-10" display="block"><mml:mrow><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">I</mml:mi><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x03B3;</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">x</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-10">Eq. (10)</xref>, the term CI is the Consistency Index and c is the range of factors comparable. The following step consists of a random index (RI) calculation of the consistency ratio (CR). This can be achieved by the following <xref ref-type="disp-formula" rid="eqn-11">Eq. (11)</xref>:</p>
<p><disp-formula id="eqn-11">
<label>(11)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-11.png"/><tex-math id="tex-eqn-11"><![CDATA[$${\rm \; \; CR\; } = {\rm \; CI}/{\rm RI}$$]]></tex-math><mml:math id="mml-eqn-11" display="block"><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">R</mml:mi><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">I</mml:mi></mml:mrow><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mrow><mml:mi mathvariant="normal">R</mml:mi><mml:mi mathvariant="normal">I</mml:mi></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>When CR &#x003C; 0.1, the matrix generate outcome is relatively consistent. Where the random index (RI) taken from the Saaty Random Index.</p>
<p><bold><italic>Step 3:</italic></bold> Through the defuzzification procedure, after processing of a remarkably consistent matrix, the TFN values are converted into observable values. In this study the procedure of defuzzification has been used [<xref ref-type="bibr" rid="ref-26">26</xref>] as described in <xref ref-type="disp-formula" rid="eqn-12">Eqs. (12)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-14">(14)</xref>, commonly known as <italic>alpha-cut</italic> method.</p>
<p><disp-formula id="eqn-12">
<label>(12)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-12.png"/><tex-math id="tex-eqn-12"><![CDATA[$${{\rm \mu }_{{\rm \alpha },{\rm \beta }}}\left( {{\eta _{{\rm ij}}}} \right){\rm \; } = {\rm \; }\left[ {{\rm \beta }.\eta {\rm \alpha }\left( {{\rm c}{1_{{\rm ij}}}} \right) + {\rm \; }\left( {1 - {\rm \beta }} \right).{\rm \; }\eta {\rm \alpha }\left( {{\rm c}{3_{{\rm ij}}}} \right)} \right]{\rm \; \; }$$]]></tex-math><mml:math id="mml-eqn-12" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mi>&#x03BC;</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mi>&#x03B2;</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mrow><mml:mi>&#x03B2;</mml:mi></mml:mrow><mml:mo>.</mml:mo><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x002B;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi>&#x03B2;</mml:mi></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>where, 0 &#x2264; &#x03B1; &#x2264; 1 and 0 &#x2264; &#x03B2; &#x2264; 1</p>
<p>Such that,</p>
<p><disp-formula id="eqn-13">
<label>(13)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-13.png"/><tex-math id="tex-eqn-13"><![CDATA[$$\eta {\rm \alpha }\left( {{\rm c}{1_{{\rm ij}}}} \right) = {\rm \; }\left( {{\rm c}{2_{{\rm ij}}} - {\rm c}{3_{{\rm ij}}}} \right).{\rm \alpha } + {\rm c}{1_{{\rm ij}}}$$]]></tex-math><mml:math id="mml-eqn-13" display="block"><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mo>&#x002B;</mml:mo><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>1</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p><disp-formula id="eqn-14">
<label>(14)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-14.png"/><tex-math id="tex-eqn-14"><![CDATA[$${\rm  }\eta {\rm \alpha }\left( {{\rm c}{3_{{\rm ij}}}} \right) = {\rm c}{3_{{\rm ij}}} - {\rm \; }\left( {{\rm c}{3_{{\rm ij}}} - {\rm c}{2_{{\rm ij}}}} \right).{\rm \alpha }$$]]></tex-math><mml:math id="mml-eqn-14" display="block"><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mi>&#x03B7;</mml:mi><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>3</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mi mathvariant="normal">c</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mn>2</mml:mn><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo><mml:mrow><mml:mi>&#x03B1;</mml:mi></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>For the identification of the domain specialist options, the previously measurements equations were applied by <italic>&#x03B1; and &#x03B2;</italic>.</p>
<p><bold><italic>Step 4:</italic></bold> The ANP approach discusses dependence among both within a cluster and between different clusters. The objective of this strategy is to formulate the <italic>supermatrix</italic> resulted from comparative analysis between groups such as goal, factors, sub-factors and alternative solutions originating from the choice vector.</p>
<p><bold><italic>Step 5:</italic></bold> To determine an alternative&#x2019;s overall performance for a TOPSIS fixed factor, this formula needs that the whole decision matrix must be in normalized form.</p>
<p><disp-formula id="eqn-15">
<label>(15)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-15.png"/><tex-math id="tex-eqn-15"><![CDATA[$${{\rm X}_{{\rm ij}}} = {\rm \; }\displaystyle{{{{\rm x}_{{\rm ij}}}} \over {\sqrt {\mathop \sum \nolimits_{{\rm i} = 1}^{\rm m} {\rm x}_{{\rm ij}}^2} }}$$]]></tex-math><mml:math id="mml-eqn-15" display="block"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">X</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:msqrt><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">x</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:msqrt></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</alternatives></disp-formula></p>
<p>In the above <xref ref-type="disp-formula" rid="eqn-15">Eq. (15)</xref>, <italic>i &#x003D; 1, 2,&#x2026;. m; and j &#x003D; 1,2, . . . n</italic>.</p>
<p>Afterward, the Normalized Weighted-Decision Matrix is generated (<xref ref-type="disp-formula" rid="eqn-16">Eq. (16)</xref>).</p>
<p><disp-formula id="eqn-16">
<label>(16)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-16.png"/><tex-math id="tex-eqn-16"><![CDATA[$${\rm }{{\rm M}_{{\rm ij}}}{\rm \; } = {{\rm w}_{\rm i}}{{\rm X}_{{\rm ij}}}$$]]></tex-math><mml:math id="mml-eqn-16" display="block"><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">M</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">w</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">X</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>where, i &#x003D; 1, 2, &#x2026; m and j &#x003D; 1,2, &#x2026; n.</p>
<p><bold><italic>Step 6:</italic></bold> Assessment of <italic>I&#x002B; matrix positive-ideal solution</italic>, and <italic>I- matrix negative-ideal solution</italic>.</p>
<p><disp-formula id="eqn-17">
<label>(17)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-17.png"/><tex-math id="tex-eqn-17"><![CDATA[$$\eqalign{{{\rm I}^ + } = {\rm \; z}_1^ + ,{\rm z}_2^ + ,{\rm z}_3^ + \ldots ..{\rm z}_{\rm n}^ +\\{{\rm I}^ - } = {\rm \; z}_1^ - ,{\rm z}_2^ - ,{\rm z}_3^ - \ldots ..{\rm z}_{\rm n}^ -}$$]]></tex-math><mml:math id="mml-eqn-17" display="block"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">I</mml:mi></mml:mrow><mml:mo>&#x002B;</mml:mo></mml:msup></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:msubsup><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x002B;</mml:mo></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x002B;</mml:mo></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mn>3</mml:mn><mml:mo>&#x002B;</mml:mo></mml:msubsup><mml:mo>&#x2026;</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mo>&#x002B;</mml:mo></mml:msubsup><mml:mspace linebreak="newline"></mml:mspace><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">I</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:msup></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:msubsup><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mn>2</mml:mn><mml:mo>&#x2212;</mml:mo></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mn>3</mml:mn><mml:mo>&#x2212;</mml:mo></mml:msubsup><mml:mo>&#x2026;</mml:mo><mml:mo>.</mml:mo><mml:mo>.</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">n</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:msubsup></mml:math>
</alternatives></disp-formula></p>
<p>In the above <xref ref-type="disp-formula" rid="eqn-17">Eq. (17)</xref><inline-formula id="ieqn-1"><alternatives><inline-graphic xlink:href="ieqn-1.png"/><tex-math id="tex-ieqn-1"><![CDATA[$,\; z_j^ +$]]></tex-math><mml:math id="mml-ieqn-1"><mml:mo>,</mml:mo><mml:mspace width="thickmathspace"></mml:mspace><mml:msubsup><mml:mi>z</mml:mi><mml:mi>j</mml:mi><mml:mo>&#x002B;</mml:mo></mml:msubsup></mml:math>
</alternatives></inline-formula> <italic>is Max zij if j</italic> is an improvement aspect, <italic>and Max zij if j</italic> is a cost aspect; <inline-formula id="ieqn-2"><alternatives><inline-graphic xlink:href="ieqn-2.png"/><tex-math id="tex-ieqn-2"><![CDATA[${\rm z}_{\rm j}^-$]]></tex-math><mml:math id="mml-ieqn-2"><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">j</mml:mi></mml:mrow><mml:mi mathvariant="normal">_</mml:mi></mml:msubsup></mml:math>
</alternatives></inline-formula> is Min zij if j is an improvement aspect as well as Min zij if j is a cost aspect.</p>
<p><bold><italic>Step 7:</italic></bold> The very next move is to measure the discrepancy among the importance of each option and the positive and also the negative-ideal solution:</p>
<p>The positive-ideal solution:</p>
<p><disp-formula id="eqn-18">
<label>(18)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-18.png"/><tex-math id="tex-eqn-18"><![CDATA[$${\rm D}_{\rm i}^ + = {\rm \; }\sqrt {\mathop \sum \nolimits_{{\rm j} = 1}^{\rm m} {{\left( {{\rm z}_{\rm i}^ + - {{\rm z}_{{\rm ij}}}} \right)}^2}} {\rm \; };{\rm i} = 1,2,3 \ldots .{\rm m}$$]]></tex-math><mml:math id="mml-eqn-18" display="block"><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x002B;</mml:mo></mml:msubsup><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:msqrt><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">j</mml:mi></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x002B;</mml:mo></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo>&#x2026;</mml:mo><mml:mo>.</mml:mo><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>The Negative-ideal solution:</p>
<p><disp-formula id="eqn-19">
<label>(19)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-19.png"/><tex-math id="tex-eqn-19"><![CDATA[$${\rm D}_{\rm i}^ - = {\rm \; }\sqrt {\mathop \sum \nolimits_{{\rm j} = 1}^{\rm m} {{\left( {{{\rm z}_{{\rm ij}}} - {\rm z}_{\rm i}^ - } \right)}^2}} {\rm \; };{\rm \; \; \; \; \; where},{\rm \; i} = 1,2,3 \ldots .{\rm m}$$]]></tex-math><mml:math id="mml-eqn-19" display="block"><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:msubsup><mml:mo>&#x003D;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:msqrt><mml:msubsup><mml:mrow><mml:mo movablelimits="false">&#x2211;</mml:mo></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">j</mml:mi></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:msubsup><mml:mo>&#x2061;</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mi mathvariant="normal">j</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace></mml:mrow><mml:mo>;</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">w</mml:mi><mml:mi mathvariant="normal">h</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mspace width="thickmathspace"></mml:mspace><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo>&#x2026;</mml:mo><mml:mo>.</mml:mo><mml:mrow><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math>
</alternatives></disp-formula></p>
<p>In the above <xref ref-type="disp-formula" rid="eqn-18">Eq. (18)</xref><inline-formula id="ieqn-3"><alternatives><inline-graphic xlink:href="ieqn-3.png"/><tex-math id="tex-ieqn-3"><![CDATA[$,\; D_j^ + \;$]]></tex-math><mml:math id="mml-ieqn-3"><mml:mo>,</mml:mo><mml:mspace width="thickmathspace"></mml:mspace><mml:msubsup><mml:mi>D</mml:mi><mml:mi>j</mml:mi><mml:mo>&#x002B;</mml:mo></mml:msubsup><mml:mspace width="thickmathspace"></mml:mspace></mml:math>
</alternatives></inline-formula><italic>expresses the Positive-Ideal solution distance for i selection</italic>, and also in <xref ref-type="disp-formula" rid="eqn-19">Eq. (19)</xref> <inline-formula id="ieqn-4"><alternatives><inline-graphic xlink:href="ieqn-4.png"/><tex-math id="tex-ieqn-4"><![CDATA[$D_i^ -$]]></tex-math><mml:math id="mml-ieqn-4"><mml:msubsup><mml:mi>D</mml:mi><mml:mi>i</mml:mi><mml:mo>&#x2212;</mml:mo></mml:msubsup></mml:math>
</alternatives></inline-formula> <italic>is the distance from the ideal-negative approach</italic>. Quantify the value of every alternative solution of the performance (Pi) (<xref ref-type="disp-formula" rid="eqn-20">Eq. (20)</xref>).</p>
<p><disp-formula id="eqn-20">
<label>(20)</label><alternatives>
<graphic mimetype="image" mime-subtype="png" xlink:href="eqn-20.png"/><tex-math id="tex-eqn-20"><![CDATA[$${\rm P} = \displaystyle{{{\rm D}_{\rm i}^ - } \over {{\rm D}_{\rm i}^ - - {\rm D}_{\rm i}^ + }}$$]]></tex-math><mml:math id="mml-eqn-20" display="block"><mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mo>&#x003D;</mml:mo><mml:mstyle scriptlevel="0" displaystyle="true"><mml:mrow><mml:mfrac><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x2212;</mml:mo></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">D</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi></mml:mrow><mml:mo>&#x002B;</mml:mo></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:mstyle></mml:math>
</alternatives></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-20">Eq. (20)</xref>, i &#x003D; 1, 2, 3&#x2026;.m</p>
<p>The step-wise sequential evaluation process referred to above would be followed by the implementation of the Fuzzy-ANP TOPSIS method, with a set of available alternatives to determine the effect of the COVID-19 on various software industries.</p>
</sec>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Data Interpretation and Findings</title>
<p>The impact of COVID-19 on different software industry factors evaluated with the help of fuzzy-ANP-TOPSIS method. This process includes <xref ref-type="disp-formula" rid="eqn-1">Eqs. (1)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-20">(20)</xref>, and is detailed below:</p>
<p>The authors in this article produced some statistical findings with the help of uniform Saaty scale shown in the <xref ref-type="table" rid="table-2">Tab. 2</xref> along with the use of <xref ref-type="disp-formula" rid="eqn-1">Eqs. (1)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-9">(9)</xref>, converted the textual words into numeric measurable representation. The triangular fuzzy numeric (TFN) values were then combined. <xref ref-type="disp-formula" rid="eqn-3">Eqs. (3)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-6">(6)</xref> were used to turn correct numerical values into fuzzy TFN values. In addition, the Level-1 variable comparative matrix is calculated in the pairs. Afterward, <xref ref-type="disp-formula" rid="eqn-10">Eqs. (10)</xref>&#x2013;<xref ref-type="disp-formula" rid="eqn-20">(20)</xref> were used for evaluating both the accuracy metrics and the random index (RI) of the formulas. A matrix for pair-wise comparisons has a random index of below 0.1, which implies that the matrix is pair-wise (<xref ref-type="table" rid="table-3">Tabs. 3</xref>&#x2013;<xref ref-type="table" rid="table-8">8</xref>).</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Fuzzy based pairwise comparison matrix</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th></th>
<th>IC1</th>
<th>IC2</th>
<th>IC3</th>
<th>IC4</th>
<th>IC5</th>
<th>IC6</th>
<th>IC7</th>
</tr>
</thead>
<tbody><tr>
<td>IC1</td>
<td>1.00000, 1.00000, 1.00000</td>
<td>0.56110, 0.66120, 0.75130</td>
<td>1.74140, 2.34130, 2.91440</td>
<td>0.61740, 0.93574, 1.06457</td>
<td>0.49475, 0.65457, 0.84472</td>
<td>1.04525, 1.00470, 1.00747</td>
<td>0.4450, 0.51450, 0.66450</td>
</tr><tr>
<td>IC2</td>
<td>0.50140, 0.65450, 0.94254</td>
<td>1.00000, 1.00000, 1.00000</td>
<td>1.18450, 1.47560, 1.87527</td>
<td>0.79598, 0.96856, 1.14858</td>
<td>1.46145, 1.86450, 2.22450</td>
<td>1.33788, 1.52785, 1.80787</td>
<td>1.55450, 2.20450, 2.85045</td>
</tr><tr>
<td>IC3</td>
<td>1.16140, 1.67120, 1.96130</td>
<td>0.53045, 0.68450, 0.85470</td>
<td>1.00000, 1.00000, 1.00000</td>
<td>1.09858, 1.34859, 1.87898</td>
<td>1.61547, 2.34758, 3.15478</td>
<td>0.34778, 0.43775, 0.57857</td>
<td>1.40470, 1.82478, 2.45759</td>
</tr><tr>
<td>IC4</td>
<td>0.34170, 0.43150, 0.58650</td>
<td>0.88457, 1.04457, 1.26470</td>
<td>0.53470, 0.74450, 0.53456</td>
<td>1.00000, 1.00000, 1.00000</td>
<td>1.54578, 1.93589, 2.35589</td>
<td>0.95859, 1.08865, 1.64589</td>
<td>1.25457, 1.64457, 2.03458</td>
</tr><tr>
<td>IC5</td>
<td>0.32250, 0.41250, 0.59230</td>
<td>0.45456, 0.54450, 0.69450</td>
<td>1.14580, 1.56459, 1.81589</td>
<td>0.42089, 0.52079, 0.67077</td>
<td>1.00000, 1.00000, 1.00000</td>
<td>1.19860, 1.54880, 2.03589</td>
<td>1.14581, 1.49447, 1.90548</td>
</tr><tr>
<td>IC6</td>
<td>0.38220, 0.48230, 0.63240</td>
<td>0.56750, 0.66470, 0.75470</td>
<td>1.74010, 2.34020, 2.99030</td>
<td>0.61078, 0.93075, 1.06075</td>
<td>0.49459, 0.65589, 0.84568</td>
<td>1.00000, 1.00000, 1.00000</td>
<td>0.40457, 0.51457, 0.66441</td>
</tr>
<tr>
<td>IC7</td>
<td>1.10240, 1.56470, 1.81457</td>
<td>0.35745, 0.45457, 0.64758</td>
<td>0.41040, 0.55070, 0.71047</td>
<td>0.49047, 0.61045, 0.80045</td>
<td>0.53589, 0.67589, 0.84586</td>
<td>1.51568, 1.96589, 2.51568</td>
<td>1.00000, 1.00000, 1.00000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-4">
<label>Table 4</label>
<caption>
<title>Defuzzification by using alpha-cut method</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th></th>
<th>IC1</th>
<th>IC2</th>
<th>IC3</th>
<th>IC4</th>
<th>IC5</th>
<th>IC6</th>
<th>IC7</th>
<th>Weightage</th>
</tr>
</thead>
<tbody><tr>
<td>IC1</td>
<td>1.00000</td>
<td>1.77145</td>
<td>0.89145</td>
<td>2.56478</td>
<td>2.66458</td>
<td>2.34474</td>
<td>0.93652</td>
<td>0.28800</td>
</tr><tr>
<td>IC2</td>
<td>0.56245</td>
<td>1.00000</td>
<td>1.72541</td>
<td>1.21145</td>
<td>1.85452</td>
<td>1.79475</td>
<td>2.41145</td>
<td>0.18900</td>
</tr><tr>
<td>IC3</td>
<td>1.12457</td>
<td>0.57100</td>
<td>1.00000</td>
<td>0.98457</td>
<td>2.60454</td>
<td>0.69457</td>
<td>2.12124</td>
<td>0.16500</td>
</tr><tr>
<td>IC4</td>
<td>0.39454</td>
<td>0.82457</td>
<td>1.01475</td>
<td>1.00000</td>
<td>2.17744</td>
<td>0.77745</td>
<td>1.89425</td>
<td>0.13300</td>
</tr><tr>
<td>IC5</td>
<td>0.37457</td>
<td>0.54741</td>
<td>0.38585</td>
<td>0.45589</td>
<td>1.00000</td>
<td>1.82457</td>
<td>1.76745</td>
<td>0.25740</td>
</tr><tr>
<td>IC6</td>
<td>0.42741</td>
<td>0.55457</td>
<td>1.44745</td>
<td>1.29765</td>
<td>0.54457</td>
<td>1.00000</td>
<td>1.43645</td>
<td>0.11890</td>
</tr><tr>
<td>IC7</td>
<td>1.07156</td>
<td>0.41245</td>
<td>0.47357</td>
<td>0.52652</td>
<td>0.56652</td>
<td>0.69458</td>
<td>1.00000</td>
<td>0.09046</td>
</tr>
<tr>
<td colspan="9">CR &#x003D; 0.07200</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-5">
<label>Table 5</label>
<caption>
<title>Global weights</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Attributes</th>
<th>Global weights</th>
<th>Global priorities</th>
</tr>
</thead>
<tbody><tr>
<td>IC1</td>
<td>0.189124</td>
<td>2</td>
</tr><tr>
<td>IC2</td>
<td>0.207457</td>
<td>1</td>
</tr><tr>
<td>IC3</td>
<td>0.185145</td>
<td>3</td>
</tr><tr>
<td>IC4</td>
<td>0.165471</td>
<td>4</td>
</tr><tr>
<td>IC5</td>
<td>0.112455</td>
<td>5</td>
</tr><tr>
<td>IC6</td>
<td>0.072456</td>
<td>6</td>
</tr>
<tr>
<td>IC7</td>
<td>0.067892</td>
<td>7</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-6">
<label>Table 6</label>
<caption>
<title>Subjective cognition results of evaluators in linguistic terms</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Attributes/Alternatives</th>
<th>SA1</th>
<th>SA2</th>
<th>SA3</th>
<th>SA4</th>
<th>SA5</th>
<th>SA6</th>
<th>SA7</th>
</tr>
</thead>
<tbody><tr>
<td>IC1</td>
<td>6.27000, 8.27000, 9.45000</td>
<td>3.91000, 5.91000, 7.55000</td>
<td>3.18000, 5.18000, 7.00000</td>
<td>1.64000, 3.36000, 5.36000</td>
<td>1.18000, 3.00000, 5.00000</td>
<td>4.45000, 6.45000, 8.00000</td>
<td>1.18000, 3.00000, 5.00000</td>
</tr><tr>
<td>IC2</td>
<td>3.18000, 5.18000, 7.00000</td>
<td>1.64000, 3.36000, 5.36000</td>
<td>1.18000, 3.00000, 5.00000</td>
<td>4.45000, 6.45000, 8.00000</td>
<td>1.18000, 3.00000, 5.00000</td>
<td>3.00000, 4.82000, 6.55000</td>
<td>0.64000, 2.27000, 4.27000</td>
</tr><tr>
<td>IC3</td>
<td>4.82000, 6.82000, 8.27000</td>
<td>1.00000, 2.64000, 4.64000</td>
<td>0.64000, 2.27000, 4.27000</td>
<td>3.00000, 4.82000, 6.55000</td>
<td>0.64000, 2.27000, 4.27000</td>
<td>3.55000, 5.36000, 7.00000</td>
<td>0.36000, 1.73000, 3.73000</td>
</tr><tr>
<td>IC4</td>
<td>4.09000, 6.09000, 7.73000</td>
<td>0.73000, 2.27000, 4.27000</td>
<td>0.36000, 1.73000, 3.73000</td>
<td>3.55000, 5.36000, 7.00000</td>
<td>0.36000, 1.73000, 3.73000</td>
<td>4.45000, 6.45000, 8.00000</td>
<td>1.18000, 3.00000, 5.00000</td>
</tr><tr>
<td>IC5</td>
<td>3.18000, 5.18000, 7.00000</td>
<td>1.64000, 3.36000, 5.36000</td>
<td>1.18000, 3.00000, 5.00000</td>
<td>4.45000, 6.45000, 8.00000</td>
<td>1.18000, 3.00000, 5.00000</td>
<td>3.00000, 4.82000, 6.55000</td>
<td>0.73000, 2.45000, 4.45000</td>
</tr><tr>
<td>IC6</td>
<td>3.55000, 5.55000, 7.27000</td>
<td>0.82000, 2.45000, 4.45000</td>
<td>0.73000, 2.45000, 4.45000</td>
<td>3.00000, 4.82000, 6.55000</td>
<td>0.73000, 2.45000, 4.45000</td>
<td>3.00000, 4.82000, 6.55000</td>
<td>0.64000, 2.27000, 4.27000</td>
</tr>
<tr>
<td>IC7</td>
<td>4.82000, 6.82000, 8.27000</td>
<td>1.00000, 2.64000, 4.64000</td>
<td>0.64000, 2.27000, 4.27000</td>
<td>3.00000, 4.82000, 6.55000</td>
<td>0.64000, 2.27000, 4.27000</td>
<td>3.55000, 5.36000, 7.00000</td>
<td>0.36000, 1.73000, 3.73000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-7">
<label>Table 7</label>
<caption>
<title>The weighted normalized fuzzy-decision matrix</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Attributes/Alternatives</th>
<th>SA1</th>
<th>SA2</th>
<th>SA3</th>
<th>SA4</th>
<th>SA5</th>
<th>SA6</th>
<th>SA7</th>
</tr>
</thead>
<tbody><tr>
<td>IC1</td>
<td>0.02800, 0.07200, 0.12000</td>
<td>0.07400, 0.10700, 0.13400</td>
<td>0.06800, 0.10400, 0.13400</td>
<td>0.02800, 0.07200, 0.12000</td>
<td>0.07400, 0.10700, 0.13400</td>
<td>0.06800, 0.10400, 0.13400</td>
<td>0.04800, 0.08700, 0.12900</td>
</tr><tr>
<td>IC2</td>
<td>0.01300, 0.04500, 0.08200</td>
<td>0.03800, 0.06200, 0.08300</td>
<td>0.03800, 0.06500, 0.09000</td>
<td>0.01300, 0.04500, 0.08200</td>
<td>0.03800, 0.06200, 0.08300</td>
<td>0.03800, 0.06500, 0.09000</td>
<td>0.06800, 0.10400, 0.13400</td>
</tr><tr>
<td>IC3</td>
<td>0.01300, 0.04700, 0.09000</td>
<td>0.04400, 0.07100, 0.09600</td>
<td>0.04400, 0.07500, 0.10600</td>
<td>0.01300, 0.04700, 0.09000</td>
<td>0.04400, 0.07100, 0.09600</td>
<td>0.04400, 0.07500, 0.10600</td>
<td>0.03800, 0.06500, 0.09000</td>
</tr><tr>
<td>IC4</td>
<td>0.02400, 0.04600, 0.07000</td>
<td>0.04400, 0.06600, 0.08400</td>
<td>0.01100, 0.03500, 0.06700</td>
<td>0.00500, 0.02800, 0.06100</td>
<td>0.04000, 0.06100, 0.07900</td>
<td>0.02400, 0.04600, 0.07000</td>
<td>0.06800, 0.10400, 0.13400</td>
</tr><tr>
<td>IC5</td>
<td>0.01400, 0.04300, 0.07900</td>
<td>0.01300, 0.04500, 0.08200</td>
<td>0.03800, 0.06200, 0.08300</td>
<td>0.03800, 0.06500, 0.09000</td>
<td>0.01300, 0.04500, 0.08200</td>
<td>0.03800, 0.06200, 0.08300</td>
<td>0.03800, 0.06500, 0.09000</td>
</tr><tr>
<td>IC6</td>
<td>0.02000, 0.05500, 0.09500</td>
<td>0.01300, 0.04700, 0.09000</td>
<td>0.04400, 0.07100, 0.09600</td>
<td>0.04400, 0.07500, 0.10600</td>
<td>0.01300, 0.04700, 0.09000</td>
<td>0.04400, 0.07100, 0.09600</td>
<td>0.04400, 0.07500, 0.10600</td>
</tr>
<tr>
<td>IC7</td>
<td>0.05100, 0.07000, 0.08300</td>
<td>0.02400, 0.04600, 0.07000</td>
<td>0.04400, 0.06600, 0.08400</td>
<td>0.01100, 0.03500, 0.06700</td>
<td>0.00500, 0.02800, 0.06100</td>
<td>0.04000, 0.06100, 0.07900</td>
<td>0.02400, 0.04600, 0.07000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="table-8">
<label>Table 8</label>
<caption>
<title>Closeness coefficients to the aspired level among the different alternatives</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Alternatives</th>
<th>d&#x002B;i</th>
<th>d&#x2212;i</th>
<th>Ci</th>
</tr>
</thead>
<tbody><tr>
<td>SA1</td>
<td>0.16142</td>
<td>0.07552</td>
<td>0.31215</td>
</tr><tr>
<td>SA2</td>
<td>0.24124</td>
<td>0.11895</td>
<td>0.32425</td>
</tr><tr>
<td>SA3</td>
<td>0.23458</td>
<td>0.07545</td>
<td>0.21245</td>
</tr><tr>
<td>SA4</td>
<td>0.45457</td>
<td>0.16658</td>
<td>0.27859</td>
</tr><tr>
<td>SA5</td>
<td>0.47758</td>
<td>0.17569</td>
<td>0.27854</td>
</tr><tr>
<td>SA6</td>
<td>0.17596</td>
<td>0.06785</td>
<td>0.28457</td>
</tr>
<tr>
<td>SA7</td>
<td>0.34578</td>
<td>0.09578</td>
<td>0.25658</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>According to the findings of this research study as presented in <xref ref-type="table" rid="table-8">Tab. 8</xref> and <xref ref-type="fig" rid="fig-4">Fig. 4</xref>, the Closeness Coefficient (Ci) of different alternatives is estimated as- 0.31215, 0.32425, 0.21245, 0.27859, 0.27854, 0.28457 and 0.25658 for SA1, SA2, SA3, SA4, SA5, SA6 and SA7, respectively. The findings show that SA2 software industry factor is highly affected by the impact of COVID-19 pandemic.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title>Graphical representation of the closeness coefficients for alternatives</title>
</caption>
<graphic mimetype="image" mime-subtype="png" xlink:href="fig-4.png"/>
</fig>
</sec>
<sec id="s5">
<label>5</label>
<title>Validations of Results</title>
<sec id="s5_1">
<label>5.1</label>
<title>Sensitivity Analysis</title>
<p>For every scientific research study, an interpretation of the findings obtained from the various viewpoints is crucial. The procedure of sensitivity analysis is one of the most efficient and reliable methods for authenticating the relevance of the outcome [<xref ref-type="bibr" rid="ref-21">21</xref>,<xref ref-type="bibr" rid="ref-23">23</xref>,<xref ref-type="bibr" rid="ref-24">24</xref>]. The proposed analysis utilized seven experimental studies in this research study to evaluate sensitivity, since the first level of hierarchy does have seven factors. At the time of testing, the sensitivity weights of all aspects were dissimilar, and at the same time, the other weights and degree of satisfaction were constant. The assessed outcome of the significant sensitivity analysis step can be seen in <xref ref-type="table" rid="table-9">Tab. 9</xref>.</p>
<table-wrap id="table-9">
<label>Table 9</label>
<caption>
<title>Sensitivity analysis</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Alternatives</th>
<th>Original weights</th>
<th>IC1</th>
<th>IC2</th>
<th>IC3</th>
<th>IC4</th>
<th>IC5</th>
<th>IC6</th>
<th>IC7</th>
</tr>
</thead>
<tbody><tr>
<td>SA1</td>
<td>0.34600</td>
<td>0.30140</td>
<td>0.24810</td>
<td>0.28200</td>
<td>0.29230</td>
<td>0.24810</td>
<td>0.28200</td>
<td>0.29230</td>
</tr><tr>
<td>SA2</td>
<td>0.35940</td>
<td>0.34600</td>
<td>0.30700</td>
<td>0.31230</td>
<td>0.31340</td>
<td>0.30700</td>
<td>0.31230</td>
<td>0.31340</td>
</tr><tr>
<td>SA3</td>
<td>0.24300</td>
<td>0.35940</td>
<td>0.33200</td>
<td>0.31530</td>
<td>0.30800</td>
<td>0.33200</td>
<td>0.31530</td>
<td>0.30800</td>
</tr><tr>
<td>SA4</td>
<td>0.30140</td>
<td>0.24300</td>
<td>0.20240</td>
<td>0.21360</td>
<td>0.21820</td>
<td>0.20240</td>
<td>0.21360</td>
<td>0.21820</td>
</tr><tr>
<td>SA5</td>
<td>0.34600</td>
<td>0.30700</td>
<td>0.31230</td>
<td>0.31340</td>
<td>0.30700</td>
<td>0.31230</td>
<td>0.31340</td>
<td>0.31450</td>
</tr><tr>
<td>SA6</td>
<td>0.35940</td>
<td>0.33200</td>
<td>0.31530</td>
<td>0.30800</td>
<td>0.33200</td>
<td>0.31530</td>
<td>0.30800</td>
<td>0.31610</td>
</tr>
<tr>
<td>SA7</td>
<td>0.24300</td>
<td>0.20240</td>
<td>0.21360</td>
<td>0.21820</td>
<td>0.20240</td>
<td>0.21360</td>
<td>0.21820</td>
<td>0.21460</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s5_2">
<label>5.2</label>
<title>Comparison of Results</title>
<p>Comparative analysis is also an essential part for confirming the effectiveness of the tactics applied by a researcher. We have used other associated method called the classical ANP-TOPSIS to undertake a comparative analysis of the results. We used this data for evaluation to gauge the observations via these techniques. It shows the reflection of the results collected from multiple different methods on the radar chart. The study results outlined in the following table show a strong similarity between all the observations from other techniques [<xref ref-type="bibr" rid="ref-21">21</xref>]. It indicates that the Fuzzy-based method provides similar research results over the regular methods. The following <xref ref-type="table" rid="table-10">Tab. 10</xref> demonstrates the comparison of fuzzy ANP-TOPSIS results with the Classical ANP-TOPSIS approach.</p>
<table-wrap id="table-10">
<label>Table 10</label>
<caption>
<title>Comparison through classical ANP-TOPSIS technique</title>
</caption>
<table>
<colgroup>
<col/>
<col/>
<col/>
</colgroup>
<thead>
<tr>
<th>Alternatives</th>
<th>Fuzzy ANP-TOPSIS</th>
<th>Classical ANP-TOPSIS</th>
</tr>
</thead>
<tbody><tr>
<td>SA1</td>
<td>0.31215</td>
<td>0.29645</td>
</tr><tr>
<td>SA2</td>
<td>0.32425</td>
<td>0.30475</td>
</tr><tr>
<td>SA3</td>
<td>0.21245</td>
<td>0.19745</td>
</tr><tr>
<td>SA4</td>
<td>0.27859</td>
<td>0.27859</td>
</tr><tr>
<td>SA5</td>
<td>0.27854</td>
<td>0.25265</td>
</tr><tr>
<td>SA6</td>
<td>0.28457</td>
<td>0.28458</td>
</tr>
<tr>
<td>SA7</td>
<td>0.25658</td>
<td>0.26548</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s6">
<label>6</label>
<title>Discussion</title>
<p>In order to prevent the transmission of COVID-19, all regional and federal governments worldwide suspended both the international and domestic travel. Besides this, most of the countries adopted temporary phases of shutdowns/lockdowns as a means to break the chain of transmission and reduce the Coronavirus cases. Numerous religious, educational, cultural, professional, sports and mass political conventions such as the conferences, festivals, Olympic games, etc., were cancelled. These countermeasures have undoubtedly been successful in containing the spread of the pandemic. As per the findings of this study, the software industry did not respond to the pandemic with increased responsiveness. Notably, as per the experts, ambivalence is not appropriate for the industry structure amidst the looming threat of the pandemic and the alerts about hand-washing and cleanliness, social separation and staying home need to be adhered to. Respondents also noted that perhaps the software industry does have a remarkable ability to follow the rules. Moreover, the respondents have faith in the government, the healthcare system and medical facilities and the consistency of the nation&#x2019;s decisions in fighting the COVID-19 pandemic. In addition, the respondents were also mindful of the information being disseminated by the media platforms about the accurate implementation of strategies to contain COVID-19. The findings show that the <italic>Government administration based software application</italic> is the <italic>worst</italic> affected factor due to the pandemic. This is software application or the administration constraints that the people are now facing due to COVID-19 pandemic. The other Software application categories that have been influenced can be ranked in the following descending order as per their ranking: <italic>Non-profit, IT &#x0026; Security, Education, Insurance, Financial and Healthcare</italic>.</p>
<p>The battle against COVID-19 is a prolonged one and is likely to affect different spectrums of software industry. Moreover, given the magnitude of disruption and upheaval that this pandemic has unleashed, some of the consequences could be far reaching and may be tabulated at a much later date. In such an unpredictable scenario, individuals require perseverance and strength to preserve positive communication and also to satisfy their essential necessities without any problems. Our study has been carried out in the early stages. It is very important that individuals who are stranded in different places or facing isolation due to quarantine impositions remain perseverant so as to thrive in the prevalent social construct at this tragic time. Most pertinently perhaps, information should be given or action needs to be taken to improve the service trust associated with economic initiatives.</p>
</sec>
<sec id="s7">
<label>7</label>
<title>Conclusion</title>
<p>In summary, COVID-19 is a worldwide concern which calls for workable and prompt solutions from not only each country&#x2019;s governments but citizens and communities as well. Government agencies must provide the public with exact information that would help them to cope up with this serious infection. Citizens in turn must religiously follow the guidelines laid down by their respective State governments. Continuous medical research and dedicated management initiatives to restrict the spread of the COVID-19 are mandatory. Any further damage likely to be done by COVID-19 pandemic can be controlled through sustained preventive mechanisms that will be successful only with societal participation. The COVID-19 disease outbreak has had a number of different impacts on the whole planet. Every individual has been hit in one form or another; some have gone bankrupt, others have lost their loved ones. The Software industry has not been and is not likely to be debilitated by COVID-19 in the near future, but, like every other industry, due to the worldwide pandemic it has certainly seen some adjustments. The Software industry has already dealt with negative issues and has emerged more resilient than before. Coronavirus tends to intensify the introduction of technology in the workplaces and the increase is likely to persist even after the COVID-19 disease outbreak. Implementing robots and AI has the potential to keep companies running in the phases of social distancing as well as significantly reduce security related risks to the users. Hence the overall impact of the pandemic on the software industry has not been voluminous. Moreover, should the industry invest in more AI mechanisms, better outcomes can be accomplished.</p>
</sec>
</body>
<back>
<ack>
<p>The authors would like to thank the Deanship of Scientific Research at Taif University, Kingdom of Saudi Arabia, for their funding support under Grant No.: 1-441-53.</p>
</ack><fn-group>
<fn fn-type="other">
<p><bold>Funding Statement:</bold> The Deanship of Scientific Research at Taif University, Kingdom of Saudi Arabia.</p>
</fn>
<fn fn-type="conflict">
<p><bold>Conflicts of Interest:</bold> The authors declare that they have no Conflicts of Interest to report regarding the present study.</p>
</fn>
</fn-group>
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