完备Brouwerian格上Fuzzy关系方程有极小解的条件  

Conditions Under Which a Fuzzy Relational Equation has Minimal Solutions ina Complete Brouwerian Lattice

作　　者：王学平[1] 

机构地区：[1]四川师范大学数学系

出　　处：《数学进展》2002年第3期220-228,共9页Advances in Mathematics（China）

基　　金：四川省教委重点资助项目.

摘　　要：本文在有限论域上对完备Brouwerian格上Fuzzy关系方程极小解的存在问题作了探讨.首先构造了Fuzzy关系方程有解但无极小解的一个例子,然后在解集非空时给出了对Fuzzy关系方程的每一个解都存在一个小于等于它的极小解的一个充分条件及一个充要条件.特别地,在充分条件下给出了一类Fuzzy关系方程所有极小解的个数的公式.In this paper, the existence of minimal solutions of a fuzzy relational equation in a complete Brouwerian lattice has been investigated in a finite case. An example of a fuzzy relational equation which has solutions but no a minimal solution is presented first. Then a sufficient condition, and a sufficient and necessary condition that for each X ∈x3, there exists a minimal element X* ∈X3 such that X*≤X are given, respectively when the solution set X3 of the fuzzy relational equation A⊙X = b is unempty. In particular, the number of distinct minimal elements of X3 is formulated under the sufficient condition.

关 键 词：完备BROUWERIAN格 FUZZY关系方程 极小解 

分 类 号：O159[理学—数学]