Abstract
This paper deals with a new type of fuzzy open-like set, viz., fuzzy β-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 α-open set [4] and fuzzy β-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 β-b-regular space, fuzzy β-b-open set coincides with fuzzy open set. In the last section some applications of the functions defined here are established.
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