The fuzzy topological spaces on a fuzzy space (Q1808922)

The author proposes a definition of fuzzy topology. In this definition a notion of fuzzy topology is considered on a fuzzy subspace [\textit{K. A. Dib}, Inf. Sci. 80, No. 3-4, 253-282 (1994; Zbl 0832.20088)] as a collection of fuzzy subspaces satisfying conditions similar to Chang-fuzzy topology [\textit{C. L. Chang}, J. Math. Anal. Appl. 24, 182-190 (1968; Zbl 0167.51001)]. Although, in this new setting, some of the fundamental results are achieved, no mention is available as to whether the present approach has a merit from the categorical point of view.