四川师范大学学报（自然科学版）2013，Vol.36Issue(2)：185-189,5.DOI:10.3969/j.issn.1001-8395.2013.02.005
BL-代数上sup-*合成模糊关系方程的极小解与算法
Minimal Solutions of Fuzzy Relational Equations with sup-* Composition on BL-Algebra and Their Algorithm
摘要
Abstract
In this paper, the problem of solving a system of fuzzy relational equations A ⊙ X = B defined on a BL-algebra is investigated (where " ⊙" denotes sup- * composition, A = (aq)I×J is a known coefficient matrix, B = (bj)j∈J is a known row vector, X = (xi)i∈1 , is a unknown row vector, and I,] are finite index sets). The relationships between the minimal solutions of the equation and the Binding-components and between the minimal solutions of the equation and the irredundant coverings are discussed. It is proved that there is a one-to-one mapping between all minimal solutions of the equation and the irredundant coverings. Moreover, an algorithm for solving all minimal solutions of the fuzzy equations is proposed by finding all the irredundant coverings.关键词
模糊关系方程/BL-代数/极小解/Binding-分量/无冗余覆盖Key words
fuzzy relational equation/ BL-algebra/ minimal solution/ Binding components/ irredundant covering分类
数理科学引用本文复制引用
曾中海,吴莉,王学平..BL-代数上sup-*合成模糊关系方程的极小解与算法[J].四川师范大学学报（自然科学版）,2013,36(2):185-189,5.基金项目
国家自然科学基金(11171242)、教育部博士点基金(20105134110002)和四川省杰出青年科技基金(2011JQ0055)资助项目 （11171242）
