模糊偏伪度量的表现定理及应用

The representation theorem of fuzzy partial pseudo-metric spaces and it's applications

本文借助概率分布函数的点式运算研究了模糊偏伪度量的表现定理,证明了由模糊偏伪度量空间(X,P,*)导出的右连续的映射族{pt}t∈(0,1)都是偏伪度量当且仅当(X,P,∧)也是模糊偏伪度量空间,进一步研究了此表现定理导出的模糊化拓扑空间。

In this paper, we research the representation theorem of the fuzzy partial pseudo-metric by the pointwise operation of distance distribution function. We prove that {pt}t∈（0,1） induced by the fuzzy partial pseudo-metric （X,P, ＊ ） are a family of partial pseudo-metric spaces if and only if （X,P, ∧ ） is a fuzzy partial pseudo-metric space. We also study fuzzifying topological spaces induced by the representation theorem too.