Measures of noncompactness for fuzzy sets in fuzzy topological spaces (Q1965330)

Recently \textit{S. G. Gal} introduced and studied some measures of non-compactness for fuzzy subsets of metric and fuzzy metric spaces [J. Fuzzy Math. 2, No. 3, 623-634 (1994; Zbl 0818.54006); 3, No. 4, 941-947 (1995; Zbl 0870.54006); 5, No. 2, 309-320 (1997; Zbl 0890.54006)]. On the other hand, \textit{I. Kupka} and \textit{V. Toma} introduced the measure of noncompactness for subsets of topological spaces [Rev. Roum. Math. Pures Appl. 40, No. 5-6, 455-461 (1995; Zbl 0855.54033)]. The main purpose of this paper is, basing on the ideas of Kupka and Toma, to define and to study some measures of non-compactness for fuzzy subsets of (Chang) fuzzy topological spaces endowed with a \(t\)-norm. In the last section the property of upper semicontinuity of a mapping \(f:X\to [0,1]^Y\) where \(X\) is a topological space, and \(Y\) is a fuzzy topological space, is studied using the introduced measures of noncompactness.