Categories isomorphic to the category of $L$-fuzzy closure system spaces

Document Type : Research Paper


School of Mathematics, Beijing Institute of Technology, 5 South Zhong- guancun Street, Haidian District, 100081 Beijing, P.R. China


In this paper, new definitions of $L$-fuzzy closure
 operator, $L$-fuzzy interior operator, $L$-fuzzy remote neighborhood
 system, $L$-fuzzy neighborhood system and $L$-fuzzy quasi-coincident neighborhood system
 are proposed. It is proved that the category of $L$-fuzzy closure spaces, the category of $L$-fuzzy interior spaces, the category of $L$-fuzzy remote neighborhood
 spaces, the category of $L$-fuzzy quasi-coincident neighborhood spaces, the category of $L$-fuzzy
 neighborhood spaces are all isomorphic to the category
 $L$-{\bf FCS} of $L$-fuzzy closure system spaces.


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