The challenge of medical diagnosis can be framed as a multiple attribute group decision-making problem, wherein the goal is to identify the most suitable solution from a range of alternatives, guided by evaluation data supplied by multiple experts across various assessment attributes [24]. In this context, the alternatives correspond to potential diseases, while the attributes encapsulate the symptoms associated with or indicative of these diseases. By integrating collective expertise and input from multiple experts, decision-makers can navigate the complex web of symptoms and diseases more effectively, leveraging diverse perspectives to arrive at a comprehensive and accurate diagnosis. This approach not only enhances the diagnostic process by considering a multitude of factors but also promotes collaborative decision-making, harnessing the collective wisdom and insights of multiple stakeholders to optimize patient care and outcomes. Artificial intelligence has emerged as a promising approach to solving complex multi-criteria group decision-making problems and deep learning stands as one of the most advanced AI frameworks. While machine learning can achieve outstanding performance, its lack of transparency in how conclusions are reached may render it unsuitable for many applications, particularly in the medical domain. This paper [25] explores different AI models and frameworks within the medical field, examining their strengths and limitations. Fuzzy logic theory has been previously used for the problem of medical diagnosis in a plethora of articles [26–30] and particularly in addressing challenges related to Multi-Criteria Group Decision-Making [8,31,32]. The MCGDM process when incorporating uncertainty and fuzzy logic theory, can be explained in two steps [24].

The initial phase of the medical decision-making process involves the articulation and handling of decision-related information. Fuzzy sets have emerged as a valuable tool in addressing numerous medical applications, offering versatile solutions to complex problems. In the realm of medical diagnosis, one prominent application involves determining the disease most likely affecting a patient based on fuzzy relations. This entails representing the relationships between symptoms and diseases, as well as between patients and symptoms, within a fuzzy medical knowledge base. These relationships are often depicted as fuzzy sets, and in the context of this article, as advanced fuzzy sets, specifically q-ROFS or IVq-ROFS. Such representations enable a nuanced understanding of the interconnectedness between symptoms and diseases, facilitating more accurate and insightful medical decision-making processes. By leveraging fuzzy sets, decision-makers can navigate the inherent uncertainty and ambiguity in medical data, thereby enhancing diagnostic accuracy and patient care.

In the group decision-making process, gathering the opinions of all decision-makers is essential, followed by employing an appropriate method to aggregate these opinions [18]. Aggregation operators serve as indispensable tools in this regard, allowing the combination of multiple fuzzy sets into a single fuzzy set [3,33]. Specifically, in the context of medical diagnosis, these operators are utilized to aggregate the q-ROFSs associated with each criterion or symptom for every disease or patient outlined in the medical knowledge and patient symptom matrices. Scholars have extensively explored various aggregation operators, including fuzzy aggregation operators. IF aggregation operators, PF aggregation operators, and q-ROF aggregation operators [18]. With the continuous advancement of IVq-ROFSs, the aggregation of IVq-ROF information gains increasing significance.

Recent studies by Wang et al. [34] have delved into four forms of IVq-ROF aggregation operators, investigating their applications in multiple-attribute group decision-making scenarios. Similarly, Ju et al. [35] have explored IVq-ROF weighted averaging aggregation operators [35]. Another type of aggregation operator is the Heronian mean and its generalized form, which considers the interdependent phenomena among the aggregated arguments [36–38]. However, while averaging aggregation operators exert a notable influence on overall data, they may lack the ability to effectively characterize individual data points [18]. On the other hand, geometric aggregation operators are more discernible in their impact on specific data points. Nonetheless, due to their operational constraints, geometric aggregation operators may introduce significant distortion to the evaluation information. Thus, selecting an appropriate aggregation operator necessitates a careful consideration of the specific context and objectives of the decision-making process to ensure accurate and meaningful results.

A critical precursor to the aggregation process in medical diagnosis is the determination of symptom weights, which holds paramount importance in ensuring an accurate and comprehensive diagnostic assessment. Employing the entropy method provides a structured and objective approach to assigning these weights, thereby guaranteeing a fair and balanced consideration of each symptom’s relevance [39]. Through the entropy method, decision-makers analyze the variability and uncertainty inherent in each symptom, enabling the identification of key factors pivotal to the diagnostic process. This systematic approach not only aids in prioritizing symptoms based on their informational contributions but also enhances the transparency and objectivity of the decision-making process [39]. Ultimately, by leveraging the entropy method to calculate weights, professionals can optimize diagnostic accuracy, leading to more precise and effective patient care and outcomes.

In the second stage of the decision-making process, the challenge lies in effectively ranking decision schemes amidst the inherent fuzziness of human cognition and the complexity of the decision-making environment [24]. Given the difficulty in completely and accurately describing decision-making information, the form of information expression directly influences the precision of evaluation. Moreover, the weight of experts cannot be disregarded during the processing of evaluation information, encompassing both the significance of the experts themselves and the rationalization of their evaluation results.

Fuzzy logic augments its diagnostic capabilities by employing similarity measures to aid in disease detection [40]. These measures, integral across various disciplines, quantify the similarity or distance between objects, facilitating comparisons based on their attributes. Developed using fuzzy sets and extended fuzzy sets like q-ROFS, similarity measures typically utilize distances and are expressed as numerical values [41]. As the similarity between data samples increases, the numerical value of the measure rises, ranging between zero and one, where zero signifies low similarity and one denotes high similarity. For example, [16], Chen [42] proposed a similarity function F to measure the degree of similarity between fuzzy sets. Wang [43] proposed new fuzzy similarity measures on fuzzy sets and elements. Later from the continuation of research of fuzzy sets Atanasov [44] presented intuitionistic fuzzy sets. That step promoted the development of similarity measures that utilize advanced fuzzy sets. Wei et al. [45,46] proposed similarity measures based on a cosine function using advanced fuzzy sets for making a medical decision. Muthukumar et al. [47] used weighted similarity measures in medical diagnosis, while Iancu [48] used similarity measures based on the Frank t-norms family.

Scores and accuracy offer an additional avenue for deriving results, incorporating degrees of membership and non-membership. Scores are particularly useful for comparing two q-ROFS, with the highest score indicating a patient’s affliction with a particular disease. In cases of equal scores, accuracy serves as the deciding factor. This article introduces a novel approach to this method termed the inverse score [49], where the lowest score designates the patient’s disease. Again, in instances of tied scores, accuracy determines the ultimate outcome, providing a comprehensive framework for decision-making in medical diagnosis.

In this work, three aggregation operators are proposed: q-ROFWA, q-ROFWG, and the q-ROFWNA paired with three ranking methods: the similarity measure, the score function, and the inverse score function. These methodologies were applied with various q-rung values, performing a sensitivity analysis to understand how the methodologies behave as q changes. While recent literature typically employs a maximum q value of 3, our analysis is extended to larger q-rung values, allowing for a broader spectrum of uncertain possibilities and providing a clearer picture of each methodology’s behavior. Additionally, a multiple criteria group decision-making analysis is conducted using the BUI granule technique. This approach generated new medical data tables with different uncertainty values, effectively simulating the diverse opinions of various experts.

Previous articles have studied the aggregation operators that are applied in our methodologies, but all of them focused on group decision-making using pre-existing decision matrices. In contrast, the BUI methodology is used to create these matrices. Another novel aspect of our approach was the use of the inverse score function, which helped overcome the unique limitations associated with the standard score function.

The organization of this paper is as follows:

In Section 2, the foundational knowledge necessary to understand the methods applied later is analyzed. The operation of q-Rung Orthopair Fuzzy Sets is explained, along with how they differ from Interval-Valued q-Rung Orthopair Fuzzy Sets. The application of the BUI rule is discussed, depending on the data form used. Additionally, the three ranking methods employed in the sensitivity analysis are examined. The specific data utilized in this paper are then described, followed by an introduction to the multiple criteria decision-making process. This section also includes an analysis of the three criteria aggregation operators and the entropy method used to calculate the criteria weights required for the MAGDM process.

In Section 3, the results produced by each methodology discussed earlier are presented. Firstly, ranking tables for the similarity measure and score function are provided using all the aggregation operators, and bar diagrams are included to graphically illustrate ranking differences. Secondly, the BUI method is applied to the medical data tables, creating various tables with different certainty values. The decision-makers are evaluated, and the optimal q-rung value is determined using the similarity measure and score function ranking methods. Lastly, a sensitivity analysis is conducted with different q-rung values across all aggregation operators and decision-making methods, ranking the diseases for each patient. To better explain the results of the sensitivity analysis, they are presented using a spider plot.

Let X be a universe of discourse. A q-ROFS A in X is given by [14,50]: A={⟨x,µA(x),νA(x)⟩,|x∈X}where µA:X→[0,1] denotes the degree of membership and vA:X→[0,1] the degree of nonmembership of the element x∈X to the set A with the condition that 0≤µA(x)q+νA(x)q≤1. The degree of indeterminacy is πA(x)=(1−μAq(x)−νAq(x))1/q where q≥1.

q-ROFS Mathematical Operations

Considering that n=(μn,vn) and φ=(μφ,vφ) are two q-ROFNs, with σ ≥ 0, q ≥ 1, the below mathematical operations could be defined [51]:

n∪φ=(max(μn,μφ),min(vn,vφ))

IVq-ROFSs offer a more flexible way of articulating opinions compared to q-ROFSs [17]. This occurs because, in IVq-ROFSs the membership degree µ and non-membership degree ν are differentiated through subsets within the [0, 1] range, rather than relying solely on crisp numbers within that interval.

Let’s consider a universe of discourse, denoted by P={p1,p2,…,pn}. An IVq-ROFS, represented by R~ on P, takes the form: R~={⟨p,µ~R(p),ν~R(p)⟩,|p∈P}where µ~R(p) represents the interval of membership degree ν~R(p) represents the interval of non-membership degree, µR(p)C[0,1],νR(p)C[0,1] and 0≤sup{µR(p)q}+sup{νR(p)q}≤1.

To simplify the lower and upper bounds of µ~R(p) and ν~R(p), will be denoted as μR−(p),μR+(p),vR−(p),vR+(p). Because of that R~ can be presented as: R~={⟨p,[μR−(p),μR+(p)],[vR−(p),vR+(p)]⟩,|p∈P}with the condition that 0≤μR+(p)q+νR+(p)q≤1 and q ≥ 1.

IVq-ROFS Mathematical Operations

Considering that n=([μn−,μn+],[vn−,vn+]) and φ=([μφ−,μφ+],[vφ−,vφ+]) are two IVq-ROFNs, with σ ≥ 0, q ≥ 1, the bellow mathematical operations could be defined [18,50]:

n¯=([vn−,vn+],[μn−,μn+])

BUI in the form ⟨x;c⟩ where x ∈ [0, 1] is an observed datum and c ∈ [0, 1] is its reliability or degree of certainty. The pair ⟨x;c⟩∈[0,1]×[0,1]. If c=0, which represents that we are fully unsure or uncertain about the value x we give, then actually x can be soundly expressed as the full unit interval [0, 1]. If c=1, which represents that we are fully sure or certain about the value x we give, then actually x should indeed be itself, an exact real value belonging to [0, 1]. BUI is a newly introduced uncertain concept that can quantify the uncertainty/certainty involved in a piece of given data information by using a real number in the unit interval [0, 1]. The basic uncertain information can measure the quality of the datum by using the degree of certainty. BUI [21] provides an effective and simple way to describe assessments or observations with a certainty degree but not the restriction on the probability measure of the first component. It can also be seen that the degree of certainty provides a measure on the quality of information. Certainty degrees can have different meanings in different decisional scenarios. For example, a large certainty degree may indicate that the decision maker has large confidence over the obtained value a or show the extent to which the value a is precisely measured or exactly collected. Each BUI value ⟨x;c⟩ can be represented as a closed interval.

Definition: A BUI granule is a pair ⟨x;c⟩∈[0,1]2 in which x∈[0,1] is a concerned evaluation value and c∈[0,1] is the certainty degree of x and 1−c∈[0,1] is the uncertainty degree of x. Let L([0,1])={[a,b]|0≤a≤b≤1} be the set of all closed intervals contained in the unit interval. We have introduced the interval transformation T. T:B→Iwhere B: BUI and I: Integral T(⟨x;c⟩)=[a,b]=[cx,cx+1−c]which might be more suitable in different decisional scenarios where the length of an interval often can be recognized as the amount of the involved uncertainty. It can be easily observed that the length of ⟨x;c⟩ is b−a equals to the uncertainty degree, 1−c.

The score and accuracy are a way to compare and rank two fuzzy numbers, while both concepts include the degrees of membership and non-membership. They can be used on q-ROFNs and IVq-ROFNs alike.

Another approach to decision-making involves similarity measures, a tool for comparing q-ROFSs that may exhibit varying degrees of overlap or similarity [54–56]. q−ROFC(A,B)=1n∑i=1nμAq(xi)∗μBq(xi)+vAq(xi)∗vBq(xi)(μAq(xi))2+(vAq(xi))2∗(μBq(xi))2+(vBq(xi))2where n is the total number of items for each fuzzy set, and q is the q-rung.

For n = 1 and two q-ROFNs A, B where A=⟨μA,νA⟩, B=⟨μB,νB⟩, the similarity measure equation in simplified to [55]: q−ROFC(A,B)=μAq(xi)∗μBq(xi)+vAq(xi)∗vBq(xi)(μAq(xi))2+(vAq(xi))2∗(μBq(xi))2+(vBq(xi))2

The similarity measure of two IVq-ROFNs, a1=⟨μa1,νa1⟩, a2=⟨μa2,νa2⟩, is calculated with the equation: S(a1,a2)=((μ_a1)q⋀(μ_a2)q)+((ν_a1)q⋀(ν_a2)q)+((μ¯a1)q⋀(μ¯a2)q)+((ν¯a1)q⋀(ν¯a2)q)((μ_a1)q⋁(μ_a2)q)+((ν_a1)q⋁(ν_a2)q)+((μ¯a1)q⋁(μ¯a2)q)+((ν¯a1)q⋁(ν¯a2)q)where: 0≤S(a1,a2)≤1.

The decision matrix outlines how a decision-maker’s evaluations of various alternatives are influenced by the occurrence of different, mutually exclusive states of the world, with known probabilities. Thus, these evaluations are treated as discrete random variables. Alternatives are typically assessed based on the expected values and variances of these evaluations, with the decision-maker aiming to either maximize the expected evaluation or both maximize the expected evaluation and minimize the variance [57].

In practical applications, the states of the world and the evaluations of alternatives may be imprecisely defined. It can be challenging to precisely express these evaluations due to a lack of sufficient information [57].

A decision matrix with the fuzzy states of the world and the fuzzy evaluations of the alternatives under the particular fuzzy states of the world is called a fuzzy decision matrix [58].

The following notations are used to present the q-rung orthopair decision matrix ℳ in fuzzy environment.

Let C={C1,C2,…,Cn} be a set of n different attributes (criteria, parameters), A={A1,A2,…,Am} be a set of different alternatives that should be evaluated under the set of m attributes.

A group decision-makers 𝒟={𝒟(1),𝒟(2),…,𝒟(l)},k=1,..,l. The 𝒟 decision-makers evaluate the n alternatives. Let the associated weights of the decision-makers be γ=(γ1,γ2,…,γl)T such that γk∈[0,1] and ∑k=1lγk=1.

A q-ROFN is symbolized by aij(k)=⟨μij(k),νij(k)⟩ denotes the priority values (membership degree and non-membership degree) with 0≤μij(k),νij(k)≤1 such that 0≤(μijq)(k)+(νijq)(k)≤1 for i=1,…,n, j=1,…,m,k=1,…,l,q≥1. The weight vector information corresponding to each attribute is indicated by w=(w1,w2,…,wn)T such that wi∈[0,1] and ∑i=1nwi=1.

Therefore, a q-ROFN fuzzy decision matrix can be taken as follows: ℳ=(aij(k))m×n

In the diagnostic process, assigning weights to each symptom is crucial as it reflects their respective importance in determining the underlying condition. These weights signify the relative significance of symptoms. Thus, the weighting scheme facilitates a more nuanced and informed diagnostic approach.

Distance is one of the most important tools used to measure the deviation between variables or sets, and the weighted distance measure is the most widely used approach in various fields. Thus far, many extensions of weighted distance measures have been presented [49]. These measures can be used in the MCGDM process and the fact they utilize the concept of attribute weights allows them to account for the relative importance of different criteria. This enables more nuanced and accurate decision-making by appropriately emphasizing critical factors and reducing the impact of less significant ones.

Also, for the application of the aggregation operators, as will be analyzed later, it is essential to compute the weights vector ω. These weights will be determined using the entropy method [59], which involves the steps analyzed below.

In general, evaluation criteria can be categorized into two types: benefit criteria and cost criteria. Benefit criterion means that a bigger value is more valuable whereas cost criteria are just the opposite [39]. According to [60], “The Entropy method is a generic form of Monte Carlo simulation which is applied in complicated estimation and optimization problems for minimizing the error”.

In this article, two entropy methods are analyzed through which the weighting of criteria can be achieved. Below, the steps of each of these methods are explained outlining their respective processes.

Weighting Entropy Method 1 [39] (1)

Calculation of the score values of each element of the decision matrix 1.1.

If the decision matrix consists of IVq-ROFSs the below score function could be used:S=12[2+(Membership−)q+(Membership+)q−(Non Membership−)q−(Non Membership+)q]

Ej=1m∑i=1mπijq+1−|μijq−νijq|πijq+1+|μijq−νijq|i∈[1,…,m],j∈[1,…,n]

The degree of indeterminacy is defined as follows: πijq=1−μijq−vijq

Calculate the weight of each criterion as follows: wj=1−Ejn−∑i=1nEj,j∈[1,…,n]

For both methods for the calculated weight, it should be true that 0≤wi≤1 and that ∑i=1nwi=1.

Generally speaking, a group decision-making process collects all decision-makers’ opinions, introducing a suitable method to aggregate them. Aggregation operators are utilized to combine a set of fuzzy sets into a single fuzzy set. Specifically, these operators are employed to aggregate the q-ROFSs corresponding to each criterion/symptom for every disease or patient in the medical knowledge and patient symptom matrices.

To develop aggregation operators for IVq-ROFNs, we must first understand the underlying concepts of aggregation and dual aggregation operators, as outlined in previous research by Beliakov et al. [61] and Grabisch et al. [62]. These foundational principles are crucial in ensuring that the aggregation operators maintain their essential properties, such as boundary conditions and monotonicity.

Definition 1: Mapping Agg [0,1]m→[0,1] shows an aggregation operator if:

Agg (0,…,0)=0 and Agg (1,…,1)=1 for boundary conditions.

Monotonicity: If ai≥bi(∀i), then Agg (a1,…,am)≥Agg (b1,…,bm).

Definition 2: Let Agg be called an aggregation operator for the unit interval, i.e., Agg[0,1]m→[0,1]. Then, the dual of the aggregation operator Agg is defined as:

Agg (a₁,..., a_m) = Neg(Agg (Neg(a₁),..., Neg(a_m)))

where Neg is a negation (complement) operator.

Definition 3: Let Ai (i=1,…,m) be a value from IVq-ROFSs with grades Ai=([νAi−,νAi+],[μAi−,μAi+]) where {νAi+}q+{μAi+}q≤1.

We define E=Agg (A1,…,Am) as an IVq-ROFS with membership grades E=([νE−,νE+],[μE−,μE+]) such that:

νE−=Agg (νA1−,νA2−,…,νAm−),

νE+=Agg (νA1+,νA2+,…,νAm+),

μE−=Agg (μA1−,μA2−,…,μAm−),

μE+=Agg (μA1+,μA2+,…,μAm+).

As we know, the Agg operator is closed, i.e., it maps the collection of IVq-ROFSs into an IVq-ROFS. This can be achieved by proving the following theorem using monotonicity.

Theorem 1. If E = Aggre (A₁,..., A_m) with grade E=([uE−,uE+],[vE−,vE+]), then {uE+}q+{vE+}q≤1 always holds.

Aggregation operators serve as efficient and versatile tools. Because of that various aggregation operators have been explored by researchers.

IVq-ROFWG and q-ROFWG

The q-rung (or Interval Valued q-Rung) Orthopair Fuzzy Weighted Geometric (q-ROFWG/IVq-ROFWG) aggregation operator is a mathematical tool used to combine multiple q-ROFNs into a single representative value. The q-ROFWG operator works by taking a set of q-ROFNs, each associated with a weight that reflects its importance, and then aggregating them using a geometric mean-based formula.

It could be calculated with the equation below [18]: q−ROFWGw(n1,n2,…,nn)=n1w1⊗n2w2⊗…⊗nnwnwhere w=(w1,w2,…,wn)T is the weight vector of the (n1,n2,…,nn) values. (1)

If ni is an IVq-ROFS with the form ni=([μni−,μni+],[vni−,vni+])(i=1,2,…,n) then the equation can be simplified to: IVq−ROFWGw(n1,n2,…,nn)=⟨[∏i=n1nn(μi−)wi,∏i=n1nn(μi+)wi],(1−∏i=n1nn(1−vi−)wi)1q,[(1−∏i=n1nn(1−vi+)wi)1q]⟩

The q-ROFWA Aggregation Operator is a mathematical operator used for aggregating multiple q-ROFNs while considering their associated weights [63,64].

Suppose a=(a1,a2,…,an) is a collection of q-ROF or IVq-ROF numbers and w=(w1,w2,…,wn) is the weight vector of ai,

It could be calculated with the following equation: q−ROFWA(a1,a2,…,an)=∑i=1nwiai=w1a1⊕w2a2⊕…⊕wnan (1)

If ai is an IVq-ROFS with the form ai= 〈[μ_ai,μ¯ai],[ν_ai,ν¯ai]⟩ then the equation can be simplified to: q−ROFWA(a1,a2,…,an)=⟨[(1−∏i=1n(1−μ_aiq)wi)1q,(1−∏i=1n(1−μ¯aiq)wi)1q],[∏i=1nν_αιwi,∏i=1nν¯aiwi,]⟩

The q-ROFWNA aggregation operator is a specialized tool designed to handle the aggregation of q-ROFNs. This operator is an extension of traditional fuzzy aggregation methods, incorporating normalization to improve the accuracy and effectiveness of decision-making under conditions of uncertainty [63,64].

Suppose a=(a1,a2,…,an) is a collection of q-ROF numbers with the form ai= 〈μai,vai⟩ and w=(w1,w2,…,wn) is the weight vector of ai.

It could be calculated with the following equation: q−ROFWNA(a1,…,an)=⟨∑i=1nwiμiq∑i=1nwi(μiq+viq)∗(1−∏i=1n(πiq)wi)q,∑i=1nwiviq∑i=1nwi(μiq+viq)∗(1−∏i=1n(πiq)wi)q⟩

Since the medical expert is unable to articulate his opinion regarding the significance of each criterion (symptom) for every disease, Table 1 [66] is utilized. This table connects linguistic values with a q-ROFN and allows us to convert linguistic terms into membership and non-membership values. This is a much better way to evaluate our certainty in the information a decision matrix provides [58]. For example, instead of trying to choose a membership degree for our confidence in a table of knowledge, it could simply be characterized as Important which corresponds to ⟨0.75,0.35⟩.

Medical Data and uncertainty

Uncertainty affects decision-making and appears in many different forms. As pointed out by Zadeh, uncertainty is an attribute of information [67]. The concept of information is fully connected with the concept of uncertainty. The uncertainty is generated by incomplete information when the initial data is incomplete, fuzziness or vagueness and ambiguous, fragmentary, not fully reliable, vague, contradictory, or deficient in some other way [20,68]. The physicians can assess data with words or more generally with linguistic expressions. Because words mean different things to different people, their linguistic uncertainties both to a single individual (intra-uncertainty: the variation among the individual opinions in a group of participants) and across a group of individuals (inter-uncertainty: the variation (or vagueness) in the opinions of individual participants—usually over time) must be captured by an appropriate kind of fuzzy sets [69,70]. Fuzzy sets and extensions have been used to capture the inherent uncertainty in data. For example, q-ROFS can model both interpersonal and intrapersonal uncertainties.

In this study, the uncertainties are characterized as implicit or epistemic (aka systematic) which includes two types of uncertainty. These two uncertainty types are: indeterminacy, which is a type of linguistic uncertainty of information [71], that is, intra-uncertainty and inter-uncertainty; fuzziness (or vagueness) of information, which results from imprecise boundaries of the fuzzy sets. The extension fuzzy sets, for example, q-ROFS, can model both interpersonal and intrapersonal uncertainties.

Medical knowledge

There are five diseases D = {viral fever, malaria fever, typhoid fever, stomach problems, and chest problems} and five symptoms in the universe of discourse S = {temperature, headache, stomach pain, cough, and chest pain} [16].

Using a fuzzy mathematical approach, we can represent medical knowledge in a variety of ways. Because of that, Tables 1 and 2 are used in this article.

In each cell of Table 2, every number signifies the degree of membership of the symptom for the disease. This is how Table R is constructed. Medical knowledge R associates symptoms with diseases and this knowledge is depicted in the following Table 2.

The data for Tables 3 and 4 are gathered from [27,48,72–74].