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

Tomasz Kubiak, Alexander P. Sostak


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.


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

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