Solving Min-Archimedean S-norm Fuzzy Relation Inequations With A Linear Objective Function

Along with the wide application of the optimization problems in fuzzy environment of daily life, many scholars have done a lot of research on solving fuzzy relation equations and inequalities with a linear objective function. S-norm is just as important as t-norm, but less relevant research on this kind of norm can be found in literatures. In this thesis, the problem of fuzzy relation equation with continuous min Archimedean s-norm is stud-ied, and the problem of solving this kind of fuzzy relation equation and inequalities with a linear objective function also be studied.This thesis is organized as follows:In the second chapter, the problem of fuzzy relational equations(FRE) with con-tinuous min-Archimedean s-norm is studied. Based on the analysis of the structure of solution sets, some necessary conditions of the FRE with continuous min-Archimedean s-norm composition are proposed, According to these necessary conditions. Some rules for reducing the problem size are given and an algorithm for solving the problem is de-signed. Numerical examples show that compared with the algorithm without any rules, the algorithm in this paper solves the problem more efficiently.In the third chapter, according to the feature of the linear function, we separate the original problem into sub-problems, and transform it to the problem of 0-1 integer programming.Four rules for reducing the problem size are given and the an efficient al-gorithm for solving fuzzy Archimedean s-norm relation equations with a linear objective function.Numerical examples show that this algorithm is more efficiently than that with-out any rules is given.In the fourth chapter, the problem of fuzzy relational inequalities(FRI) with continu-ous min-Archimedean s-norm is studied. Based on the analysis of the structure of solution sets, an efficient algorithm and four rules for this kind of problems is proposed.Numerical examples show that this algorithm is efficient.