非负整数格上Fuzzy关系方程的解集

The Solution Sets of a Fuzzy Relational Equation in a Nonnegative Integer Lattice

在一种特殊的完备Brouwerian格即非负整数格上对Fuzzy关系方程的解集作了深入探讨.首先讨论了解存在的条件及解集的性质,然后在解集非空时给出了整个解集,最后讨论了不同系数方程的解集的关系.

In this paper,the solution set of a finite fuzzy relational equation is incestigated in a nonnegative integer lattice which is a special complete Brouwerian lattice.First,a necessary and sufficient condition for existence of a solution and some properties of the solution set are shown.Then the solution set of the fuzzy relational equation is given in a nonnegative integer lattice when the solution set of the equation is nonempty. Finally, the relation of solution sets of some equations in which the coefficients are different is investigated.