A new approach for some applications of generalized fuzzy closed sets

Abstract

Generalized closed sets play an important role in the study of topological spaces. In the literature we have seen the relation between closed set and generalized closed set is linear in nature, both in crisp and fuzzy environment. In particular, every closed set is a generalized closed set. In this present treatise, a new type of generalized closed set via $$(i,j)^{*}$$ -fuzzy $$\gamma $$ -open set, namely $$(i,j)^{*}$$ - $$\gamma gf\gamma $$ -closed set have been introduced in a fuzzy bitopological space and interrelationships of it with the existing ones have been made. It has been proved that this newly defined generalized fuzzy closed set is totally independent with $$(i,j)^{*}$$ -fuzzy closed set. Various characterizations of this set have been established and some interesting results are cited. As applications of this set various types of continuities are studied in the same environment. More applications are proposed by introducing a new kind of closure operator namely $$(i,j)^{*}$$ - $$\gamma $$ - $$cl_{\gamma }^{*}$$ -operator and important results have been reported based on this concept.