Elsevier

Applied Soft Computing

Volume 24, November 2014, Pages 196-211
Applied Soft Computing

Group decision making in medical system: An intuitionistic fuzzy soft set approach

https://doi.org/10.1016/j.asoc.2014.06.050Get rights and content

Highlights

  • Group decision making for medical diagnosis.

  • Intuitionistic fuzzy soft set and fuzzy soft matrix.

  • Hamming distance and Euclidean approach.

  • Cardinal of intuitionistic fuzzy soft set to compute the weight.

  • Viral fever related diagnosis.

Abstract

In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.

Introduction

Disease diagnosis is one of the difficult tasks of medical science. As complex decision making, disease diagnosis involves a number of symptoms analysis, so this process sometimes takes too long time to reach conclusion of exact disease. Similarly, this might yield wrong diagnosis due to overlooking of few trivial symptoms, which leads to worse situation. To ease this complex decision making process, use of computing techniques mainly expert system has a long history with disease diagnosis. Success had been achieved respectively with those systems but problem was uncertainty modeling. All those early systems were made to handle crisp data. But in real world there is a degree of uncertainty involved in every decision making process. In 1965, proposal of fuzzy set theory by Zadeh [1] was the corner stone to solve such uncertain scenario. Since then, there are many developments in the field and researchers [2], [3] started to use fuzzy expert system for medical diagnostic procedures.

Several other methods, including statistics, pattern recognition, artificial intelligence and neural networks have been used as an aid to medical diagnosis [4], [5], [6], [7], [8], [9]. Group decision making using fuzzy soft set constitutes another approach to aid medical diagnosis. GDM using fuzzy soft set consists of multiple experts interacting with each other to reach a final conclusion based on their observations. Each decision maker might have their own thought which differs from others’ in various aspects but they should have a common goal to reach the ultimate destination. GDM problem consists of finding the best alternative(s) from a set of feasible alternatives according to the preferences provided by a group of experts. The alternatives are classified from best to worst, using the information known according to the set of experts.

Molodtsov [10] presented soft set as a completely generic mathematical tool for modeling uncertainties. He introduced the concept of soft set theory [10] similar to some other traditional tools such as the theory of probability [35], theory of fuzzy sets [1], rough set theory [36], and the interval mathematics. But all these theories have their own difficulties due to the inadequacy of the parameterization. Molodtsov [10] proposed soft set theory which is free from such kind of difficulties. Maji et al. [11], [12] pursued further investigation on soft set theory by defining some operations and established the soft set into decision making problems. As defined by Molodtsov [10], in soft set theory, initial description of any object has an approximate nature and one do not need to introduce the notion of exact solution. In several fields of sciences, engineering, economics, and medicals sciences, the soft set theory is being used very conveniently due to the absence of any restrictions on the approximate descriptions. A number of applications of soft sets are found in different fields including texture classification and business applications [13], [14], [15], [16]. Some new operations on soft set theory are given by Ali et al. [17]. The concept of soft group was introduced by Aktas and Cagman [18] in 2007. Presently, the work on soft set theory is progressing rapidly. Maji and Roy [11] addressed an application of soft set theory in decision making problems. Under Maji and Roy's inspiration, Xiao et al. [13] developed soft set theory into the research of business competitive capacity evaluation. In 2006, Mushrif et al. [14] proposed a new approach for classification of natural textures. Chen et al. [19] presented a revised definition of soft sets parameterization reduction and compared with the related concept of attribute reduction in rough sets theory. In soft set theory, the parameterization is done with the help of words, sentences etc. The parameters may not be crisp always. They may be fuzzy words or sentence involving fuzzy words. Vagueness presented in soft set demanded Fuzzy Soft Set (FSS) [20] to be evolved. Maji et al. [20] initiated the concept of fuzzy soft sets as the combination of fuzzy sets and soft sets. Roy and Maji [37] proposed fuzzy soft set theoretic approach to present the application of fuzzy soft set in decision making problem. Later, Kong et al. [38] claimed that the method presented in [37] was incorrect and proposed a revised algorithm. Satisfactory evaluation of membership values is not always possible because of the insufficiency in the available information besides the presence of vagueness situation. Also evaluation of non-membership values is also not always possible for the same reason. As a result hesitation evolves. Fuzzy soft set theory was not found suitable to solve such kind of problems. In those situations intuitionistic fuzzy soft set theory [21] was proved to be more suitable. Maji et al. [21], [39], [40] presented the notion of the intuitionistic fuzzy soft set theory which is based on a combination of the intuitionistic fuzzy set [22], [23] and soft set [10] models.

In this article, an algorithmic approach is proposed to solve group decision making problem in medical science using intuitionistic fuzzy soft set based operations. Generally, experts evaluate a set of symptoms for disease diagnosing purpose. Often it is found that the individual experts are not paying careful attention on all the symptoms, rather they express their interest only for a subset of symptoms which they think to be more significant. They often believe those subset of symptoms can efficiently fulfill their purpose. When diagnose is done in this manner, then different experts might differ in their opinions and it becomes quite difficult to properly diagnose a patient. Some expert might diagnose that the patient suffering from one disease while the other expert's opinion differs. To resolve this type of situation, we propose a method that collects all the related experts’ opinion about various possible diseases and their observed symptoms characteristics. Then a confident weight is assigned to each of the experts which depend on their prescribed opinions. We have used a novel concept using cardinal of intuitionistic fuzzy soft set to compute the weight. The proposed confident weight also reduces the chance of biasing. Once the weights are assigned to individual experts’ opinions, we present a consensus reaching approach based on intuitionistic fuzzy soft set where all experts deliver their agreement for a final disease. The correctness of the proposed approach has been validated using distance measurements and consents of a majority of experts. As many of the previous approaches, this article does not use any standard medical knowledgebase related information during decision making, rather this article rely on the information given by the experts. Only for validating the final diagnosis, we use medical knowledgebase.

The rest of this article is organized as follows. Preliminaries contains primary discussions of the various useful ideas including intuitionistic fuzzy set, distance measurements (Hamming and Euclidean), intuitionistic fuzzy soft set, intuitionistic fuzzy soft matrix and some operations on them. The proposed approach and cardinals of IFSS to solve intuitionistic fuzzy soft set based decision making problem is presented in Proposed approach section. Then Case study section includes a practical case study for clarifying our proposed method. Hamming and Euclidean distance observations to validate our approach is adhered in Validation of results using distance measurements followed by discussions and comparisons with existing works in the next section. Finally conclusions are given in last section.

Section snippets

Preliminaries

In this section, we first recall some basic ideas of intuitionistic fuzzy set, soft set and their properties. Then we point out some interesting connection between these two sets.

Proposed approach

In this section, we define cardinal of IFSS, cardinal matrix [41] and cardinal score. Then we present the proposed algorithmic approach.

Case study

The required dataset regarding this research work was collected from a local sub divisional Government hospital at Durgapur, West Bengal, India, after a detailed discussion about the various aspects of fever with the concerned experts. Experts explained how viral fever, malaria, typhoid etc. attack human inherent immune system and by which set of symptoms one can be aware about the viral attack. They extended their assistance to talk with a few patients who are suffering from the related

Validation of results using distance measurements

As stated in case study, after a fruitful discussion with the corresponding medical experts, a medical knowledgebase (Table 5) is designed in terms of intuitionistic fuzzy sets consisting of a set of disease and the related set of symptoms concerned with a specific disease. The diseases and symptoms are similar as defined in case study. The details of information are given in Table 5. According to the basis of intuitionistic fuzzy set, this article describes each symptom by two numbers:

Discussion and comparison with existing works

In this section, we briefly discuss our proposed approach and compare it with some existing methods.

Conclusion

This study has proposed an algorithm to solve group decision making problem for medical disease diagnosis using intuitionistic fuzzy soft set. The proposed algorithm is divided into two phases: first phase executes the decision making process and second phase validates the final outcome. This method has considered a set of five related diseases with a set of common symptoms. In this analysis, opinions of four experts for a particular patient were investigated using IFSM. Each expert's

Acknowledgments

The authors are very grateful to the editor-in-chief and the anonymous referees for their constructive comments and valuable suggestions, which have led to a substantial improvement of this paper.

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