$\beta$-$b$-REGULARITY IN FUZZY SETTING

This paper deals with a new type of fuzzy open-like set, viz., fuzzy $\beta$-$b$-open set, the class of which is strictly larger than that of fuzzy open set as well as fuzzy preopen set [11], fuzzy semiopen set [1], fuzzy $\alpha$-open set [4] and fuzzy $\beta$-open set [6]. However, three different types of fuzzy continuous-like functions are introduced and studied and also the mutual relationships of these functions are established. Afterwards, two new types of separation axioms and a new type of compactness are introduced and studied. It is shown that in a fuzzy $\beta$-$b$-regular space, fuzzy $\beta$-$b$-open set coincides with fuzzy open set. In the last section some applications of the functions defined here are established.