max-~*合成模糊关系方程的解集

Solution Sets of Fuzzy Relation Equations with Max-~* Composition

主要讨论[0,1]上max-*合成模糊关系方程的解集.首先,给出单个变量方程有解的充要条件.然后,讨论多变量单一方程的解集,给出方程解集非空的充要条件;在解集非空时,给出方程的极小解以及极小解的个数.最后,讨论方程组解集非空的充要条件,并且在方程组解集非空时,给出求极小解的方法和方程组的解集.

In this paper,the solution sets of fuzzy relation equations with maxcomposition are investigated on[0,1].Firstly,a necessary and sufficient condition is shown that the equation with single variable is solvable.And then,we discuss the single equation with multiple variables and obtain a necessary and sufficient condition that the equation is solvable.When the solution set is nonempty,the minimal solutions and the number of minimal solutions are obtained.Finally,a necessary and sufficient condition is shown that the equation set is solvable.When the solution set is nonempty,an algorithm for computing minimal solutions and the solution sets of the equation set are obtained.