5Operations on Fuzzy/Intuitionistic Fuzzy Sets and Application in Decision Making

5.1 Introduction

A fuzzy set may be viewed as an extension of an ordinary set where operations like union, intersection, and complement have been extended to logical operations. There are lot of operators on fuzzy sets implementing basic operations of union and intersection. Among the well‐known operations, which are performed on fuzzy sets are fuzzy union, fuzzy intersection, fuzzy complement, fuzzy algebraic sum, and algebraic product. Intuitionistic fuzzy set, which is an extension of fuzzy set, is very much useful when dealing with real‐time application that takes into account more uncertainty. Like fuzzy set, there are also few operators on intuitionistic fuzzy set. These operators are used in almost all types of applications such as fuzzy/intuitionistic fuzzy decision making, image processing, pattern recognition, linguistics, information retrieval, and so on. In addition, Zadeh [1] introduced bounded sum and bounded difference, which are used in fuzzy reasoning, decision making, pattern recognition, information retrieval, and so on.

5.2 Fuzzy Operations

In this section we will define various types of fuzzy operations. Among many operations that are defined in this section, fuzzy union, intersection, and fuzzy complements are the most common operations that are used.

5.2.1 Fuzzy Union

Union of two fuzzy sets A and B is given as:

where μA ∪ B = μ(A) ∨ μ(B).

5.2.2 Fuzzy Intersection ...

Get Fuzzy Set and Its Extension now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.