A NEW TYPE OF REGULARITY VIA FUZZY $\alpha$-PREOPEN SET

This paper deals with a new type of set, viz., fuzzy $\alpha$-preopen set, the class of which is strictly larger than that of fuzzy open set as well as fuzzy $\alpha$-open set [4]. Using this newly defined fuzzy set, here we introduce and study fuzzy $\alpha$-precontinuous and fuzzy $\alpha$-preirresolute functions. It is shown that fuzzy $\alpha$-preirresolute function is fuzzy $\alpha$-precontinuous, but the converse may not be true, in general. Next we introduce fuzzy $\alpha$-preregular space, in which fuzzy open set and fuzzy $\alpha$-preopen set coincide. Lastly, some applications of the functions defined here are established.