$\beta^{c}$-CLOSURE OPERATOR IN FUZZY SETTING

Abstract

Fuzzy $\beta$-open set is introduced in [6]. Using this concept as a basic tool, in [2] we have introduced and studied fuzzy $\beta^{*}$-closure operator and fuzzy $\beta^{*}$-closed set. Here we introduce fuzzy $\beta^{c}$-closure operator and fuzzy $\beta^{c}$-closed set. This newly defined operator is coarser than fuzzy $\beta$-closure operator [6] and fuzzy $\beta^{*}$-closure operator. Also fuzzy $\beta^{c}$-closure operator is an idempotent operator. Then some mutual relationship of this operator with the operators defined in [2, 3, 4, 5, 6, 7, 8] are established. With the help of this operator a new type of fuzzy separation axiom is introduced. Lastly we characterize this operator via fuzzy net.