Solving Fuzzy Relation Inequalities With A Linear Objective Function

Along with the wide application of the optimization problems in fuzzy environment of daily life, how to solve this kind of problems efficiently and quickly, especially opti-mization problems constrained by fuzzy relation equations, has already become one of hot topics of many scholars. In recent years, however, the study of fuzzy inequalities with general composition operator or max-strong pseudo-t-norm composition operator, and linear programming constrained by them are rarely seen in publications. In this thesis, fuzzy relation inequalities, and linear optimization problems with fuzzy relation inequality constraints are studied.This thesis is organized as follows:In the second chapter, firstly, the structure of the solutions sets of fuzzy relation inequalities(FRI) is analyzed. Two rules for simplifying the problem are introduced. An algorithm for solving the FRI with general composition is proposed. The numerical experiments are presented to illustrate the effectiveness of the algorithm.In the third chapter, we introduce FRI with max-strong pseudo-t-norm composition. It's proved that the conclusions given in the last chapter hold when the operator T is changed to strong pseudo-t-norm.In the fourth chapter, a linear optimization problem with max-strong pseudo-t-norm composition FRI constraints is considered. In order to solve the optimization problem quickly and effectively, four rules are given to simplify the calculation, and an algorithm is proposed based on them. According to different strong pseudo-t-compositions, three typ-ical numerical examples are given. The numerical experiments are presented to illustrate the efficiency of the algorithm.