Abstract
Recently, fuzzy systems have become one of the hottest topics due to their applications in the area of computer science. Therefore, in this article, we are making efforts to add new useful relationships between the selected L-fuzzy (fuzzifying) systems. In particular, we establish relationships between L-fuzzy (fuzzifying) Čech closure spaces, L-fuzzy (fuzzifying) co-topological spaces and L-fuzzy (fuzzifying) approximation spaces based on reflexive L-fuzzy relations. We also show that there is a Galois correspondence between the categories of these spaces.
Highlights
In [1], Goguen replaced the structure of membership values [0, 1] in Zadeh fuzzy sets [2]
The narrow goal of this contribution was to establish the relationship between L-fuzzy Čech closure spaces, L-fuzzy co-topological spaces, and L-fuzzy approximation spaces based on reflexive L-fuzzy relations
The category of L-fuzzy approximation spaces based on reflexive L-fuzzy relations with
Summary
In [1], Goguen replaced the structure of membership values [0, 1] in Zadeh fuzzy sets [2]. A graded approach to topology and many related structures (L-topology, L-fuzzifying topology, and L-fuzzy topology) is an essential characteristic of the spaces where sets are identified with their characteristic or lattice-valued membership functions. With the development of a weaker concept of fuzzy pretopology, the focus was changed to topological structures where the closing and opening operators are not idempotent. In fuzzy-valued topological structures, Qiao [31] showed that a Galois connection exists between the category of stratified L-Čech closure spaces and the category of reflexive L-fuzzy relation sets. Our contribution discusses these weaker structures from the categorical point of view and establishes the relationships between them.
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