Semicompactness in Fuzzy Topological Spaces

The paper deals with the concept of semicompactness in the generalized setting of a fuzzy topological space. We achieve a number of characterizations of a fuzzy semicompact space. The notion of semicompactness is further extended to arbitrary fuzzy sets. Such fuzzy sets are formulated in different ways and a few pertinent properties are discussed. Finally we compare semicompact fuzzy sets with some of the existing types of compact-like fuzzy sets. We ultimately show that so far as the mutual relationships among differ- ent existing allied classes of fuzzy sets are concerned, the class of semicompact fuzzy sets occupies a natural position in the hierarchy.