The authors deal with a new application of the “fuzzication" procedure. Their goal is to fuzzify the category TOP$(L,M)$ of $(L,M)$-topological spaces to obtain FTOP$(L,M)$. The basic properties of the fuzzy category FTOP$(L,M)$ and its objects ($(L,M)$ fuzzy $α$-topologies) are investigated by appropriate tools introduced and studied in the paper.
Reviewer: Eduardo Pascali (Lecce)