Multiobjective programming in fuzzy and intuitionistic fuzzy environment

Abstract

Decision making is one of the area applicable to almost all the branches of science, engineering, health care, business and social sciences. Many mathematical and stochastic tools are available to newlinedeal with various decision making problems, when the information available are quantitative and accurate. But in most of the real life problems, one is encountered by situations where information available are in linguistic form or imprecise and vague and thus the traditional tools of mathematics newlineand statistics fail to model such situations. Fuzzy/Intuitionistic fuzzy set theory provides a platform for modeling such situations containing the imprecision and uncertainties in the information. newlineWe divided into seven chapters. In first chapter of thesis we gave definitions of fuzzy sets, types of membership function, fuzzy numbers and various kind of fuzzy numbers. Further, we defined intu- newlineitionistic fuzzy (IF) sets, IF numbers and various kind of IF numbers, interval valued intuitionistic fuzzy (IVIF) sets. We also defined IVIF numbers and its types. Fuzzy/ intuitionistic fuzzy linear pro- gramming, fully Fuzzy linear programming, fuzzy/intuitionistic fractional programming problems newlineare also described in this chapter. The second chapter is divided into two sections. In the first section newlineof second chapter, we have given a new method for solution of multiobjective linear programming (MOLP) problem in intuitionistic fuzzy environment. The method uses computation of the upper newlinebound of a non-membership function in such way that the upper bound of the non-membership function is always less than the upper bound of the membership function of intuitionistic fuzzy number. Further, we also construct membership and non-membership function to maximize membership newlinefunction and minimize non-membership function so that we can get a more efficient solution of a probabilistic problem by intuitionistic fuzzy approach.