The Discussion Of Solutions To Fuzzy Relation Programming

In this thesis, three fuzzy relation programming problems with fuzzy coeffi-cients, including one fuzzy relation programming problem with linear objective andtwo fuzzy relation programming problems with nonlinear objective, are proposed.Based on the theory of fuzzy numbers.ranking, all three problems are converted intofuzzy relation programming problems with real coefficients by using a linear rankingfunction. Then the solutions can be obtained easily.This thesis consists of four chapters. Chapter1is an introduction. First is a briefreview of the background and current progress of fuzzy sets, fuzzy optimization andfuzzy relation programming. Then we also introduce the main content and outline ofthis thesis.In chapter2, some basic concepts and theories of fuzzy sets and fuzzy numbershave been presented. Besides, we give an introduction to linear ranking functionwhich is involved in this thesis.Chapter3introduces some basic concepts and main types of fuzzy relation e-quations and fuzzy relation programming problems. The current progress of fuzzyrelation programming is also discussed in this chapter.The last chapter, which is the key content herein, has three sections. In section1, we propose a solution to fuzzy relation linear programming problem with fuzzycoefficients. In section2, a solution to fuzzy relation nonlinear programming problemwith fuzzy coefficients is proposed.∨· composition is considered in this problem. Insection3, we propose a solution to fuzzy relation nonlinear programming with fuzzycoefficients using∨∧composition. And numerical examples are provided in allthree sections for illustration purpose.The main conclusion of this thesis is to examine the limitations and the prospectof future research directions.