Masters Theses

Kan Araki

Date of Award

12-1991

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Yueh-er Kuo

Committee Members

Steve Serbin, Tadeusz Janik

Abstract

The purpose of this paper is to investigate the theory and methods of Fuzzy Linear Programming problems. The stress of the presentation is placed on the transformation methods from fuzzy models to crisp models, and on the sensitivity analysis on fuzzy parameters. Moreover, we extend sensitivity analysis in general cases and we show a practical method to solve the problems with nonlinear membership functions. In addition to these researches, we propose the new concept in order to relate the method of Fuzzy Linear Programming with conventional methods.

The introduction discusses originality of this thesis and proposes several items for future study.

Chapter 1 discusses the basic theory of Fuzzy Sets and Fuzzy Linear Programming problems and their transformation methods to crisp models.

Chapter 2 presents sensitivity analysis on the two types of Fuzzy Linear Programming problems as well as stability study on fuzzy parameters.

Chapter 3 presents solving the problems with nonlinear membership functions by using piecewise linear functions.

Chapter 4 discusses relationship between a fuzzy programming method and a goal programming method.

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