On generalized fuzzy bitopological spaces

This paper is devoted to introduce the new classes namely generalized fuzzy bitopological spaces and defined various types of generalized pairwise fuzzy sets in the generalized fuzzy bitopological spaces. Several examples are given to investigate the generalized pairwise fuzzy sets and characterizations of generalized pairwise fuzzy sets are studied in this paper. Especially the intersection (or union) of two generalized pairwise fuzzy closed sets is also a generalized pairwise fuzzy closed set. The intersection of two generalized pairwise fuzzy nowhere dense sets is also a generalized pairwise fuzzy nowhere dense set and a generalized pairwise fuzzy nowhere dense set is a generalized pairwise fuzzy semi-closed set are established. Additionally, a generalized pairwise fuzzy nowhere dense and generalized pairwise fuzzy Fσ-set is a generalized pairwise fuzzy σ-nowhere dense set is investigated in this paper. Furthermore generalized pairwise fuzzy first category spaces, generalized pairwise fuzzy second category spaces and generalized pairwise fuzzy submaximal spaces are defined and some of whose properties are also studied in this paper.