模糊层次拓扑空间理论(Ⅰ)

The Theory of Fuzzy Stratiform Topological Spaces (I)

在模糊拓扑空间中,有些集合本身并不是闭集,但在某些层次上它却表现出闭集的特性,这就是所谓的层次闭集.层次闭集可以形成一种拓扑,称之为模糊层次拓扑.这种拓扑已在模糊拓扑学的研究中发挥了较大的作用,并逐渐形成了一种理论,谓之模糊层次拓扑空间理论.本文综述了该理论的基本框架,并分析了它的发展趋势.

The paper is continuation of [1]. For given fuzzy lattice L and its molecular a,in L-fuzzy topological space,it is defined that a stratiform closure operator, so-called GFa-closure operator,it is intorduced that a stratiform closed set,so-called GFa- closed set. The basic properties of GFa- closure operator and GFa- closed sets are discussed. It is point out that GFa- closure operator is a generalization for Rodabaugh's a- closure operator. The decomposition theorem has been presented for the closure of L-fuzzy set.