Transportation Problems in Intuitionistic Fuzzy Environment

Abstract

In the last few years, several methods have been proposed for solving different types of intuitionistic fuzzy transportation problems. In this thesis, limitations and flaws of these existing methods are pointed out. Also, to resolve the flaws as well as to overcome the limitations of the existing method, new methods are proposed. The thesis comprises seven chapters. A brief outline of the chapters is as follows: Chapter 1 Introduction Chapter 1 is introductory in nature. In this chapter, a need of intuitionistic fuzzy transportation problem as well as different types of intuitionistic fuzzy transportation problems are discussed. Furthermore, the existing methods [131,132] for solving intuitionistic fuzzy transportation problems are presented in a detailed manner. Chapter 2 A simplified method for solving intuitionistic fuzzy transportation problems of type I In this chapter, an alternative method for solving intuitionistic fuzzy transportation problems of type I is proposed. Also, the advantages of proposed method over the existing methods [9,46,48,64-66,118,132] are discussed. Furthermore, to illustrate the proposed method, the numerical examples, considered by Singh and Yadav [132], are solved by the proposed method. Chapter 3 A simplified method for solving intuitionistic fuzzy transportation problems of type II In this chapter, an alternative method for solving intuitionistic fuzzy transportation prob- lems of type II is proposed. Also, the advantages of proposed method over the existing methods [1,3,119,131], are discussed. Furthermore, to illustrate the proposed method, the numerical examples, considered by Singh and Yadav [131], are solved by the proposed method. Chapter 4 Modified approach for solving intuitionistic fully fuzzy transportation problems Kumar and Hussain [84-86] proposed methods for solving intuitionistic fully fuzzy transportation problems. In this chapter, it is pointed out that for the ranking function, used by Kumar and Hussain [84-86], the linearity property is not satisfying.