An alpha-Fuzzy Max Order and Solution of Linear Constrained Fuzzy Optimization Problems

This paper introduces a new concept, the a-fuzzy max order, and uses the concept in the study of fuzzy linear constrained optimization problems, and develops two nwnerical algorithms respectively for the determination of the feasible solution space and the solution of the fuzzy optimization problem.

Abstract

In this paper, we introduce a new concept, the a-fuzzy max order, and then use the concept in the study of fuzzy linear constrained optimization problems. For constraints given by 11 inequalities involving fuzzy numbers with isosceles triangle membership functions, we prove that the feasible solution space is determined by 3/1 non-fuzzy inequalities. For constraints involving fuzzy numbers with other forms of membership functions, we develop two nwnerical algorithms respectively for the determination of the feasible solution space and the solution of the fuzzy optimization problem. An illuminative example is also given in this paper to demonstrate the validity of the methods and algorithms developed.