凸模糊集与模糊闭集间的弱等价条件

Equivalent condition between convex fuzzy set and fuzzy closed set

在文献3所定义的凸模糊集、1定义的模糊闭集及2定义的弱似凸模糊集等概念的基础上,讨论了三种模糊集间的构成关系,得到了模糊闭集构成弱似凸模糊集的等价条件,及模糊闭集构成凸模糊集的依赖条件,从而丰富了凸模糊理论。

In this paper we intoduce the definition of convex fuzzy sets from (3), fuzzy closed set from (1) and weakly quasi-convex fuzzy set from (2). Base on those three definations, we discuss the relationships among those convex sets. We give an equivalent condition that a fuzzy closed set is a quasi-convex fuzzy set and a relate condition between quasi-convex fuzzy set and convex set. Consequently the theory of the convex fuzzy sets is enriched.