Fuzzy拓扑共生结构与预序关系

Fuzzy Syntopogenous Structures and Preorder Relations

A. Csáaszár在[1]中引入拓扑共生(Syntopogenous)结构的概念,将拓扑结构,邻近结构,一致结构适当地统一起来研究。近年来,A·K·Katsaras等人在[2,3,4]中分别提出Fuzzy序拓扑空间,Fuzzy拓扑共生空间的概念,给出了一些基本性质。在文[6]中,我们对以完全分配格L为值域的Fuzzy拓扑共生空间作了一些初步的讨论,得到包括它与L-fuzzy拓扑,邻近性,一致性的关系,连续性,连通性等的若干性质。本文将X上的L-fuzzy拓扑共生结构与X上的预序结构联系起来,讨论了L-fuzzy拓扑共生结构生成的预序,预序决定的L-fuzzy拓扑生成结构,以及递增(减)的L-fuzzy拓扑共生结构的性质;其它进一步的讨论将在随后的工作中给出。

In present paper, we introduce the L-fuzzy syntopogenous structures, where L is a Fuzzy. We combine the concepts of preorder structure and L-fuzzy syntopogenous structure. In Section 2 we study the preorder relation generated by an L-fuzzy syntopogenous structure, and the L-fuzzy syntopogenous structure defined by a preorder relation. In Section 3 we define and study some of the properties of increasing (decreasing) L-fuzzy syntopogenous spaces with preorder.