On somewhat fuzzy semicontinuous functions

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was introduced in [5] and this concept was studied in connection with the idea of feebly continuous functions and feebly open functions introduced in [4]. The purpose of this paper is to extend this concept to fuzzy topological spaces. In this connection we have introduced the concept of somewhat fuzzy semicontinuous functions and somewhat fuzzy semiopen functions and studied their properties. Also further we have introduced the concept of fuzzy semi irresolvable and fuzzy semi resolvable spaces and we have given a characterization of fuzzy semi irresolvable spaces. Several examples are given to illustrate the concepts introduced in this paper.