Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators

This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice.     

L-拓扑空间中的β-闭性

在L-拓扑空间中借助于β-开L-集合和它们的不等式给出了β-闭性的一种新形式,这里L是完备的DeMorgan代数。它也能够借助于β-闭L-集和它们的不等式刻画。当L是完全分配的DeMorgan代数时,它的许多刻画被给出了。     

L_Δ-闭包空间的Δ-仿紧性

在L_Δ-闭包空间中借助于L_α-Δ-开覆盖、α-局部有限集族、α--局部有限集族引入了Δ-仿紧性.证明了它对Δ-闭集是遗传的、Δ-紧的L_Δ-闭包空间和Δ-仿紧空间的积空间是Δ-仿紧的重要性质.     

L-拓扑空间中的α-紧度

借助于格L的蕴涵算子,在L-拓扑空间中引入了模糊集的α-紧度的概念.一个L-模糊集G是α-紧的当且仅当它的α-紧度coma(G)=(T).我们还研究了α-紧度的一系列性质.     

L-拓扑空间的新U0公理

在L-拓扑空间引入了一种新的U0公理,它被叫做次U0公理。次U0公理蕴涵次T0公理。次U0公理是一般拓扑中U0公理的好的扩张。另外,L-实直线和L-单位区间满足次U0公理。     

关于近良紧性的注记

证明近良紧性是分明近紧性的一种L-good extension。     

L-拓扑中的度量理论

对L-拓扑中已有度量理论的研究进展作一个简要的介绍和评述,力图使读者了解L-拓扑中度量理论的发展概况和发展方向。     

L-模糊集的可数starplus-紧性

本文研究了在L-拓扑空间中,利用L-拓扑的水平拓扑引入可数starplus-紧性的概念,获得了可数starplus-紧性的性质,并且对一般拓扑中可数starplus-紧性的推广.     

O-convergence of fuzzy nets and its applications

In this paper, an O-convergence theory of fuzzy nets is built in L-topological spaces by means of neighborhoods of fuzzy points. It has many nice properties. It can be used to characterize the closed set, open set, T₂ separation axiom and fuzzy compactness.     

L-拓扑空间中PS收敛理论的应用

在L-拓扑空间引入了准半连续和PS-不定序同态的概念,讨论了网和理想的PS-收敛理论的应用.