# Fuzzy MCDM: Application in Disease Risk and Prediction

## Fuzzy MCDM: Introduction

Fuzzy multi-criteria decision-making (MCDM) as a tool has been quite useful where data is huge, incomplete, and uncertain. Fuzzy-based analysis approach has been used for data mining techniques to identify patterns and formulate equations and decision trees when the data is huge, contains uncertainties, and where traditional forms of statistical analysis have failed. Medicine is one such field where a huge amount of raw, uncertain data is available. Different diseases manifest differently in patients, that is, symptoms are similar, but the quantitative and qualitative aspect of the severity of symptoms may differ, leading to uncertainty [1]. MCDM was proposed in the 1970s and it is a subdiscipline of operations research that explicitly evaluates multiple conflicting criteria in decision-making [2].

Incorporating fuzzy logic with MCDM techniques significantly enhances the quality and adaptability of decision-making, generating probabilistic values even when data is ambiguous and uncertain. Fuzzy MCDM is used as an alternative decision-making tool on multiple-criteria problems by decision-makers, where the linguistic values are represented as a fuzzy numbers and are responsible for measuring or evaluating the importance of the criteria. Although MCDM is a novel approach for solving problems with multiple conflicting criteria, it is still not implemented for decision-making on a managerial level due to certain drawbacks [3]. One of these drawbacks is that MCDM does not allow interdependency of criteria, which makes the solution obtained by the algorithms unfeasible. Unlike a strict hierarchy system, autonomous decision-makers are inclined to use more than the required number of criteria [4]. The purpose of fuzzy MCDM is to design mathematical computational tools for quantitative and qualitative evaluation of multiple and inconsistent criteria. The evaluation criteria help the decision-makers in ranking, classifying the alternatives, and choosing the best path forward. Many methods and tools are used for disease prediction and risk analysis using fuzzy MCDM. Applying and developing a fuzzy MCDM expert system for disease risk prediction has many merits, a primary one being that of preemptive mitigation steps to lessen the financial burden upon the patient [5]. The different expert system of risk prediction for diseases like heart diseases, breast cancer [6-9], and diabetic retinopathy have been developed and tested by various individuals. These systems do prove to be a viable tool for disease prediction. In this work, the architectural composition of a general fuzzy system is explored to understand how the patient’s biological data can be applied to a system as fuzzy inputs to get a crisp value output of the likely disease he/she could suffer. A new method that combines fuzzy logic with the multi-criteria decision-making system is meticulously explored. Three different case studies of applying fuzzy MCDM to disease prediction are explored and evaluated based on other state-of-the-art methods, i.e., neural networks.

This chapter is further divided into sections are proposed as: Section 4.2 describes the literature review done by many researchers. Section 4.3 focuses on the approach/methodology used in this chapter, and Section 4.4 discusses the case studies on MCDM. The chapter concludes with Section 4.5 with its future scope.

## Literature Review

Energy has a significant role in the growth of industries, technologies, and agriculture. In other ways, a country’s development (i.e., social and economic) is highly dependent on energy planning, which is a big issue for every countries. These problems are evaluated using MCDM methods. Many researchers study using the MCDM method to resolve the above mentioned problem.

In [10], I. Kaya et al. present a cumulative study on fuzzy MCDM: application and methodologies discussed by different researchers in the field of energy. They studied many research papers (who works on fuzzy MCDM method) w'ritten by different researchers to solve energy decision-making problems including parameters such as year, types of fuzzy sets, country, fuzzy MCDM method, journal, and document type. They conclude that Turkey and China are the countries where good numbers of research in field of energy-related problems (using fuzzy MCDM methods) were published. In [11], M. Cloak et al. proposed a fuzzy set based integrated MCDM model for prioritization of renewable energy alternatives (in Turkey). Authors used two methods (type-2 fuzzy AHP (analytic hierarchy process) and hesitant fuzzy TOPSIS) to analyze the weight of decision tree and prioritize the renewable energy alternatives. Further in [12], M. Yucesan et al. proposed a multi-phase MCDM model for selection of green suppliers. Weight selection measures for green suppliers are analyzed using best-w'orst method (BWM) and order ranking is analyzed by interval type-2 fuzzy technique (IT2F TOPSIS). This proposed model is implemented as a selection process for green in a plastic injection molding facility (in Turkey). In [13], C. N. Wang et al. consider a problem that occurs in the garment industry of Vietnam. In this w'ork, the authors implemented a MCDM model to enhance the selection and evaluation process for suppliers of garment industries. Some factors considered in this study were the selection of supplier as determined by a triple bottom line (TBL) model, weight of all factors as determined by the fuzzy analytical hierarchy process (FAHP) method, and TOPSIS to rank the best supplier of fabric in garment industry. The authors concluded that Decision Making Unit 10 was the best method for finding the ranking of a supplier. In [14], Y. Suh et al. worked with a new MCDM method using the Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) approach. This proposed approach evaluated the service quality of mobile for subjective (used DEMATEL method) and objective weights (used Shannon Entropy). The authors concluded that the proposed model was capable of analyzing mobile services on the basis of overall performance.

In [15], Kirti Sharawat et al. used MCDM method for determining the highest quality diet suitable for the diabetic patient. The categorization of the diet is done based on categories such as calories, body fat, and carbs. This work used an analytic hierarchical process model along with the MCDM approach for ranking the diet suitable for diabetic patients. Fuzzy TOPSIS method was used for the validation part which was developed by Wang et al. [16]. They concluded that, FI (a food type) showed better results than others. Li-En Wang et al. [17] used a new hybrid model with a combination of IVIFSs and COPRAS methods. They applied fuzzy MCDM method on a hybrid model to find and rank the risk of failure modes. The weight of risk factors was calculated by a method named IVIF-ANP by taking into consideration individual relationships. This model turned out to be more accurate and more efficient than the traditional FMEA model. A fuzzy MCDM approach was discussed by Chih-Young Hung et al. for evaluating four account receivable (A/R) collection of instruments [18]. For each case, the determination of decision criteria weights were calculated with the help of fuzzy analytic (a hierarchy process) for dealing with the subjective judgment’s qualitative attribute. The fuzzy MCDM approach enabled for efficient decision-making and synthesizing the group decision. Lazim Abdullah [19] provides a review of the various classification techniques of fuzzy MCDM. Abdullah also discusses the real-life applications of fuzzy MCDM in Malaysia.

Andrzej Piegat et al. proposed an approach for analyzing the severity of chronic liver disease using fuzzy MCDM techniques. The proposed characteristic objects method (COMET) approach was compared to the TOPSIS and AHP methods [20]. The results obtained by Piegat showed that the COMET approach gave better results as compared to the other two approaches, which was evident from the fact that the COMET approach gives 966,309 correct answers as compared to 805,345 correct answers given by TOPSIS and 933,165 correct answers given by AHP. The main implementation suggested by Cheng was an evaluation of a weapons system [21]. The two parameters for evaluating desired weapons systems in the real-world conflict in nature, that is, a tradeoff between the performance of the parameters and weapons system descriptions that are generally vague and linguistic in nature. The first problem can be solved via general MCDM techniques like AHP. For solving the second problem. Fuzzy MCDM techniques are needed. Cheng devised a general algorithm in which a judgment matrix was built by pairwise comparison of triangular fuzzy numbers, varying between 1 and 9. The eigenvectors that are present in the judgment matrix are estimated. The next section discusses the methodologies used in this chapter in detail.

## Methodologies

This section discusses the mathematical procedure of fuzzy MCDM and architecture of fuzzy MCDM inference systems.

### Mathematical Procedure for Applying Fuzzy MCDM

#### Fuzzification

Fuzzification is the term used to convert crisp input values into fuzzy input values [22]. The fuzzification process is responsible for converting scalar value into fuzzy value. It converts crisp values to membership values corresponding to the fuzzy set of the linguistic term [23]. Membership’s functions are of various types like Gaussian waveform, triangular waveform, trapezoidal, etc. A Gaussian waveform is suitable for a system that demands high accuracy, while triangular and trapezoidal functions are more suited for systems where in a short period of time significant dynamic variations occur.

#### Fuzzy Sets

Fuzzy means nothing or that cannot be predicted, for example, weather. ‘Fuzzy set’ was introduced by Lotfi A. Zadeh and Dieter Klaua in 1965. In fuzzy sets, every element has different degrees of membership *(Цл(х))* on a particular set *A* and element *x* whose limit range is between 0 and 1. In this, elements work on partial membership on a particular set [24], for example range can be between 0.0 and 1.0. When the element’s value belongs to 0.0 it shows absolutely false and 1.0 means absolutely true. Fuzzy sets are represented with a tilde (~) symbol.

#### Crisp Sets

A Crisp set is also known as a classical set. It is a collection of distinct objects in which elements have complete membership *(X* or *U)* on that particular set, for example, students passed grades or not. The range of membership is belongs to either 0 or 1. There is no partial membership available for the element set.

#### Membership Functions

A membership function (MF) is outlined as a degree of truth [25]. The representation of member function is shown in eq. (1). It’s a curve-like structure in which each input and output is mapped between values zero and one. Degree of membership is a value which is associated with the corresponding input value (i.e., the output of the membership function). Membership operator/value is shown in Figure 4.1.

### General Architecture of a Fuzzy MCDM Inference System

A fuzzy inference system (FIS) is used to map the fuzzy input set to the fuzzy output [24], shown in Figure 4.2. It is a way of applying human language reasoning with the concept of fuzzy logic incorporated in it.

For example.

If A, then *B.*

Therefore, *B.*

FIGURE 4.1 Membership function of fuzzy set [26].

FIGURE 4.2 Gaussian membership function.

This form of reasoning is fairly strict, that is, В can only be if A. Fuzzy logic loosens this strictness by implying that В can be mostly if A is mostly that is to say

If A then *В *Mostly *A*

Therefore mostly *A*

#### Fuzzy If-Then Rules

In this case, when one condition is true then other condition will show the results. For example: It is of the following form: If ‘a’ is M, then ‘b’ is N. The antecedent is ‘a’ is M; the consequence is 'b' is N.

M and N are defined by fuzzy sets on the universe of discourses R and S. Here, ‘a’ and ‘b’ refers to the input and output respectively [27]. The implication of ‘is’ work different in both the antecedent and consequence, in the antecedent ‘is’ is used to assign a value between 0 and 1 while in the consequence ‘is’ is used to assign N to ‘b’.

FIS architecture is shown in Figure 4.3. FIS includes four modules: fuzzifier, defuzzifier, inference engine (IE), and fuzzy knowledge base (FKB).

FIGURE 4.3 Fuzzy inference system architecture.

The fuzzifier converts the input crisp values of the antecedent to fuzzy sets. The inference engine gives the fuzzy output from a fuzzy input and the fuzzy knowledge base is a database that consist the rule base. The defuzzifier converts the fuzzy set obtained by the inference engine to a crisp value [28]. The next section discusses case studies for diagnosing heart disease (a medical problem) using the fuzzy MCDM method.