Fuzzy compactness via summability

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