星形模糊集的若干性质研究

The Research of Several Propositions on Starshaped Fuzzy Sets

本文从星形模糊集的定义出发,引出了拟星形模糊集和伪星形模糊集的概念,通过研究其各自重要性质给出了对应星形模糊集的若干等价判别条件;进一步,本文深入研究了它们与凸模糊集、模糊数之间的关系,丰富和完善了星形模糊集的理论。

Starting from the definition of the starshaped fuzzy set, this paper introduces the concept of fuzzy quasi-starshaped set and fuzzy pseudo-starshaped set. Some equivalent discrimination conditions on the kind of starshaped fuzzy sets are given by studying the key propositions of them. Furthermore, the relationships among convex fuzzy, fuzzy numbers and them are deeply researched, which enrich and perfect the theory of the starshaped fuzzy set.