Similarity Measure of Different Types of Fuzzy Sets

Abstract

In today’s highly competitive world, all the people compare the things with each other. Similarity measure is the concept which helps us to know how much two things are similar. For this we, firstly calculate the degree of similarity. Higher is the degree of similarity between two things, they are more similar to each other. In this thesis, similarity measure between different types of fuzzy numbers is calculated. The chapter-wise summary of the thesis is as follows:

Chapter 1 is introductory in nature. This chapter includes basics, and concepts used throughout the work.

Chapter 2 presents brief review of the work done in the area of fuzzy similarity measure problem.

In Chapter 3 we studied the similarity measure between generalized fuzzy numbers. To illustrate the presented method a numerical example is solved and also some properties of similarity measure of generalized fuzzy numbers are proved.

In Chapter 4 Similarity measure between interval-valued fuzzy sets is studied. The presented method is illustrated by solving a numerical example and some properties are proved.

Chapter 5 In this chapter similarity measure between intuitionistic fuzzy sets has been studied. Also in this chapter we give the shortcomings of some already proposed methods and to overcome those shortcomings other methods are presented. The presented method is illustrated by solving a numerical example and some properties are proved.