Solving Interval-Valued Fuzzy Relation Equations With A Linear Objective Function

At present.on the theory of fuzzy relation equation has been used more and more of practical problems,such as System Analysis,Decision-Making Theory.Fuzzy Reasoning, Fuzzy Control and so on.With deep research of the fuzzy relation equation,as the generalization of fuzzy relation equation,interval-valued fuzzy relation equation to reflect the daily reasoning of ambiguity and uncertainty are more advantages.How to solve this kind of problems in the way of convenient and efficient,especially in recent years,the optimization problem constrained fuzzy relation has become a hot.point of research.However.the study with interval-valued fuzzy relation equations of the linear programming is blank.In this paper,two optimization models with linear objective functions subject to a system of interval-valued fuzzy relation equations with max-min and max-product are presented. In what follows,we will introduce the main results of the paper briefly.1.In the second chapter,first,interval-valued fuzzy relation equation is introduced and some basic definitions are given.Then we introduce the algorithms of max-min and max-product interval-valued fuzzy relation equations respectively.Two examples are provided to illustrate the performances of our algorithms finally.For solving the linear programming problem of the third and fourth chapter provides a theoretical basis.2.The third chapter discusses an optimization model with a linear objective function subject to a system of max-min interval-valued fuzzy relation equations.We examine the effect of the cost coefficient first.Next,we convert the problem to an equivalent problem involving 0-1 integer programming.The main contents of this chapter are that,some theorems are given to simplify the original problem.We propose a method to simplify the work of computing.Two numerical examples are provided to illustrate the performance of our procedure.Numerical examples show that.the algorithm is effective.In particular,we point out that.our procedure is better than[2]and[3]in the sense of computation complexity in solving linear objective optimization subject to fuzzy relation equation. 3.The fourth chapter focuses on an optimization model with a linear objective function subject to a system of max-product interval-valued fuzzy relation equations.We examine the effect of the cost coefficient first.Next.we convert the problem to an equivalent problem involving 0-1 integer programming.Based on the theorems of this chapter,we propose a method to simplify the work of computing.The numerical example shows that the algorithm is effective.