On $ps$-$ro$ semiopen fuzzy set and $ps$-$ro$ fuzzy semicontinuous, semiopen functions

Abstract

The aim of this paper is to introduce and characterize $ps$-$ro$ semiopen (semiclosed) fuzzy sets, which are totally independent of the existing notion of fuzzy open (closed) sets and semiopen (semiclosed) fuzzy sets. Also, in term of these fuzzy sets and operators $ps$-$scl$ and $ps$-$sint$, a class of functions named as $ps$-$ro$ fuzzy semicontinuous and $ps$-$ro$ fuzzy semiopen (closed) functions are defined and their various properties are studied. $ps$-$ro$ fuzzy semicontinuity is indeed totally different from both the existing concepts of fuzzy continuity and fuzzy semicontinuity. Similarly, $ps$-$ro$ fuzzy open (closed) and well known concept of fuzzy semiopen (closed) functions do not imply each other. These concepts are used as new tools to study different characterizations of the given fuzzy topological space, giving a new dimension in the study of fuzzy topological spaces.