Generalized version of $\alpha^{\theta}$-closed set and its applications in fuzzy setting
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This paper deals with a new type of generalized version of fuzzy closed set, viz., $f\alpha^{\theta}g$-closed set, the class of which is strictly larger than that of fuzzy $\alpha$-closed set [1]. Using this concept as a basic tool, here we introduce an idempotent operator. Afterwards, $f\alpha^{\theta}g$-open (resp., $f\alpha^{\theta}g$-closed) function is introduced and characterized. It is shown that the class of $f\alpha^{\theta}g$-open (resp., $f\alpha^{\theta}g$-closed) functions is strictly larger than that of fuzzy open [2] (resp., fuzzy closed [2]) function. In the last section a new type of fuzzy separation axiom is introduced and some applications of the function defined here are established.
Abstract
This paper deals with a new type of generalized version of fuzzy closed set, viz., $f\alpha^{\theta}g$-closed set, the class of which is strictly larger than that of fuzzy $\alpha$-closed set [1]. Using this concept as a basic tool, here we introduce an idempotent operator. Afterwards, $f\alpha^{\theta}g$-open (resp., $f\alpha^{\theta}g$-closed) function is introduced and characterized. It is shown that the class of $f\alpha^{\theta}g$-open (resp., $f\alpha^{\theta}g$-closed) functions is strictly larger than that of fuzzy open [2] (resp., fuzzy closed [2]) function. In the last section a new type of fuzzy separation axiom is introduced and some applications of the function defined here are established.