Certain Investigations On Fuzzy Number Approximation And Fuzzy Linear Programming Problems

Abstract

Linear Programming LP is one of the most frequently applied newlineOperation Research techniques in real world problems The LP problems newlinein the crisp scenario aims to maximize or minimize a linear objective newlinefunction under linear constraints But in many practical situations the newlinedecision maker may not be in a position to specify the objective and or newlineconstraint functions precisely but rather can specify them in a fuzzy sense newlineIn such situations it is desirable to use some fuzzy linear programming type newlineof modeling so as to provide more flexibility to the decision maker Since newlinethe fuzziness may appear in a linear programming problem in many ways newlineeg the inequalities may be fuzzy the goals may be fuzzy or the problem newlineparameters may be in terms of fuzzy numbers the definition of newlinefuzzy linear programming problem is not unique This thesis aims to study newlinevarious types of fuzzy linear programming problems newlineThe chapter wise summary of the thesis is as follows newlineChapter 1 presents the preliminary notions of fuzzy set theory newlinenecessary background of fuzzy numbers and fundamental concepts of fuzzy newlineoptimization techniques newlineChapter 2 deals with the analysis of Nearest Symmetric newlineTrapezoidal or Triangular Fuzzy Number Approximation NSTFNA with newlinepreserving expected interval The objective of this chapter is to convert the newlinearbitrary fuzzy numbers into a NSTFNA while preserving the expected newlineinterval The converted NSTFNA is translation invariant scalar invariant newlinecontinuous monotonic and linear Further the NSTFNA can be applied for newlinefuzzy partition which is very much used to express the linguistics newlineexpressions newlineChapter 3 deals with Fuzzy Linear Programming FLP problem newlinein which the righthand side and decision variables are symmetric triangular newlinefuzzy numbers Using CR representation method the FLP problem is newlinedecomposed into two crisp Linear Programming LP problems The newlinesolution of FLP problem is obtained by solving the resultant LP problems Chapter 4 focuses on the solution procedure of the Fully Fuzzy newlineLinear Programming FFLP problem newline newline