A fuzzification of the category of M-valued L-topological spaces

Abstract

A fuzzy category is a certain superstructure over an ordinary category in which ”potential” objects and ”potential” morphisms could be such to a certain degree. The aim of this paper is to introduce a fuzzy category FTOP(L,M) extending the category TOP(L,M) of M-valued L- topological spaces which in its turn is an extension of the category TOP(L) of L-fuzzy topological spaces in Kubiak-Sostak’s sense. Basic properties of the fuzzy category FTOP(L,M) and its objects are studied.

Keywords

• M-valued L-topology
• (L,M)-fuzzy topology
• L-fuzzy category
• GL-monoid
• Power-set operators
• (L,M)-interior operator
• (L,M)-neighborhood system