This paper deals with a new type of fuzzy separation axiom, viz., fuzzy α-b-regular space by introducing fuzzy α-b-open set as a basic tool. This newly defined class of sets is strictly larger than that of fuzzy open set as well as fuzzy preopen set, fuzzy semiopen set, fuzzy α-open set and fuzzy β-open set. Also, we introduce new type of fuzzy compact space and a strong form of fuzzy T2-space. However, three different types of functions are introduced and studied. Also the mutual relationships of these functions are established. Lastly some applications of these functions on the spaces introduced here are established.