Solving Min-s-norm Fuzzy Relation Equations With A Linear Objective Function

Fuzzy relational equation is the foundation of fuzzy mathematics.It has been shown that the fuzzy relational equations serve as the key to various applications of fuzzy control and fuzzy diagnosis.Fuzzy relational equation with max-t-norm compositions were studied by many scholars.The min-s-norm compositions are as important as the max-t-norm but less well known.The optimization model with a linear objective function subject to fuzzy relation equations has been raised by fang in 1999.Since the solution set of Fuzzy relation equations is non-convex,we can not use traditional methods to solve this problem.Then the optimization model with a linear objective function subject to max=t-norm fuzzy relation equations has been converted into a 0-linteger programming problem by Fang and li.However,this method is not suitable for large-scale problems.Many scholars have improved the method.There is little literature about the optimization model with a linear objective function subject to min-s-norm fuzzy relation equations.In this paper,we concentrate on solving min-s-norm fuzzy relation equations with a linear objective function.In the second chapter,we will define the problem and introduce some concepts of fuzzy relation equation and min-s-norm.Then we will solve the max-t-norm and min-s-norm fuzzy relation equation.In the third chapter,we will introduce the optimization model with a linear objective function subject to fuzzy relation equations and solve it by 0-1 integer program and give out the algorithm.Examples will give in to illustrative how the algorithm works.In the forth chapter,we will introduce The optimization model with a linear objective function subject to min-max fuzzy relation equations and the optimization model with a linear objective function subject to min-min{a+x,1}fuzzy relation equations.Then we will Simplify the algorithm of solving the optimization model with a linear objective function subject to min-s-norm fuzzy relation equations.two examples will give to illustrate the algorithm.