Fuzzy compactness via summability

A fuzzy subset α of a fuzzy topological space is fuzzy sequentially compact if any sequence x = ( λ a n x n ) of fuzzy points in α has a generalized fuzzy subsequence which is fuzzy convergent in α . More generally we say that a fuzzy subset α of a fuzzy topological space X is G -fuzzy sequentially compact if any sequence x = ( λ a n x n ) of fuzzy points in α has a generalized fuzzy subsequence y such that G ( y ) ∈ α where G is a function from a suitable subset of the set of all sequences of fuzzy points in X . We investigate some of the basic properties of this compactness and suggest some open problems.