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 ...

We introduce the concept of fuzzy co-r-M -semicontinuous, and investigate the relationships between fuzzy co-r-M -semicontinuous mappings and several types of fuzzy r-minimal semicompactness.

in this paper, the notion of fuzzy semicompactness degrees isintroduced in $l$-fuzzy topological spaces by means of theimplication operation of $l$. characterizations of fuzzysemicompactness degrees in $l$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

In this paper, the notion of fuzzy semicompactness degrees isintroduced in $L$-fuzzy topological spaces by means of theimplication operation of $L$. Characterizations of fuzzysemicompactness degrees in $L$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

The concepts of semicompactness, countable semicompactness, and the semi-Lindelöf property are introduced in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of semiopen L-sets and their inequalities. They do not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by semiclosed L-sets and their i...