模糊关系的非循环度量

Acyclicity Measure of Fuzzy Relations

本文定义并研究了一般t-模下模糊关系的非循环指标。首先,在所涉及的t-模T左连续的情况下,讨论了T-非循环指标与T-非对称指标以及T-传递闭包的非自反指标的关系;其次,研究了模糊关系交的T-非循环指标;最后,在取小t-模下,研究了T-非循环指标与T-传递指标以及非自反指标的关系。从而将文献中的一些非循环性质推广为程度描述.

In this paper, we define and study the acyclicity indicator of fuzzy relations under a general t-norm T. Firstly, we investigate the relationships between the indicators of T-acyclicity, T-asymmetry and the reflexivity of T-transitive closure under thecondition that the involved t-norms are left continuous. Then we focus on the study of T-acyclicity indicator of the intersection of fuzzy relations. Finally, we deal with the relationships between the indicators of T-acyclicity, T-transitivity and irreflexivity with the t-norm rain. As a result, some results in the literature regarding acyclieity are extended to their degree description.