Medical Diagnosis Based on Distance Measures Between Picture Fuzzy Sets

Medical Diagnosis Based on Distance Measures Between Picture Fuzzy Sets

Palash Dutta (Department of Mathematics, Dibrugarh University, Dibrugarh, India)
Copyright: © 2018 |Pages: 22
DOI: 10.4018/IJFSA.2018100102

Abstract

This article describes how most frequently uncertainty arises due to vagueness, imprecision, partial information, etc., are encountered in medical diagnosis. To deal with this type of uncertainty, initially fuzzy set theory (FST) was explored and accordingly, medical decision making became one of the most important and interesting areas of applications of FST. Interval valued fuzzy sets (IVFSs) and intuitionistic fuzzy sets (IFS's) were developed and successfully applied in different areas including medical diagnosis. Although, IFS forms a membership degree and a non-membership degree separately in such a way that sum of the two degrees must not exceed one, but one of the important and integral part i.e., degree of neutrality is not taken into consideration in IFS, which is generally occurred in medical diagnosis. In such circumstances, picture fuzzy set (PFS) can be considered as a strong mathematical tool, which adequate in situations when human opinions involved more answers of type: yes, abstain, no. For this purpose, this article, proposes some distance measures on PFS and studies some of its properties. Also, an attempt has been made to carry out medical diagnosis via the proposed distance measures on PFSs and exhibit the technique with a suitable case study. It is found that the distance measures make it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.
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1. Introduction

It is observed that real world problems are usually tainted with uncertainty arises due to lack of knowledge, imprecision, partial information. To deal with such uncertainty Zadeh (1965) developed a tool, which is well known as FST. Basically, in real life situations, due to the imprecise nature of medical documents and uncertain information gathered for decision making requires the use of fuzzy. In FST, to each element of the universe of discourse a degree of membership between 0 and 1 is assigned. However, it is not always possible for a membership function of the type IJFSA.2018100102.m01 to precisely assign one point from [0,1] so it is more realistic to assign interval value. People believe that assigning an exact number to expert’s opinion is too restrictive and the assignment of an interval valued is more realistic (Gehrke et al., 1996). In such situations, IVFS can be considered as an extended version of FST. The concept of IVFS was first presented by Sambuc (1975) in his doctoral research (thesis) names as IJFSA.2018100102.m02fuzzy set. Thereafter, an important generalization of FST has been made by Atanassov (1986) and termed IFS. IFS ascribe a membership degree and a non-membership degree separately in such a way that sum of the two degrees must not exceed one. It is observed that fuzzy sets are IFSs but converse is not necessarily correct. Later, Cuong and Kreinovich (2013) introduced PFS which is a direct extension of FST and IFS by incorporating the concept of positive, negative and neutral membership degree of an element.

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