Abstract
The aim of this paper is to study L-fuzzy closure operator in Lfuzzy topological spaces. We introduce two kinds of L-fuzzy closure operators from different point view and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-FCTOP.
Highlights
Since Chang [2] introduced fuzzy set theory to topology, many researchers have tried successfully to generalize the theory of general topology to the fuzzy setting with crisp methods
It is an pity that their closure operators are defined by the level L-topology of the L-fuzzy topology, not by L-fuzzy topology itself
The aim of this paper is to study L-fuzzy closure operators in L-fuzzy topological spaces in different ways from [3, 7, 13]
Summary
Since Chang [2] introduced fuzzy set theory to topology, many researchers have tried successfully to generalize the theory of general topology to the fuzzy setting with crisp methods. In [15], we established fuzzy remote neighborhood systems in L-fuzzy co-topology and prove that TFRNS is isomorphic to L-FCTOP. It is well-known that clsoure operator (or clsoure system) plays an important role in topology and it is a very good way to characterize topology. It is an pity that their closure operators are defined by the level L-topology of the L-fuzzy topology, not by L-fuzzy topology itself. The aim of this paper is to study L-fuzzy closure operators in L-fuzzy topological spaces in different ways from [3, 7, 13]. We give two kinds of L-fuzzy closure operators and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-FCTOP
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