r-τ12-θ-GENERALIZED FUZZY CLOSED SETS IN SMOOTH BITOPOLOGICAL SPACES

Year 2015, Issue: 4, 60 - 73, 01.05.2015

Osama A. E. Tantawy Rasha N. Majeed Sobhy A. El-sheikh

Abstract

− In [34] we introduced the notion of r-(τi, τj)-θ-generalized fuzzy closed sets in smoothbitopological spaces by using (τiθ-fuzzy closure, denoted Cθon smooth bitopological spaces by using smooth supra topological space(X, τ12) which is generated from smooth bitopological space (X, τ1, τ) [1], such that Cθ≤ Tτi. Inthis paper, we introduce a new class of r-θ-generalized fuzzy closed sets, namely, r-τ12-θ-gfc in smoothbitopological spaces via Cθ-fuzzy closure operator. The basic properties of these sets are studied.Furthermore, the relationship with other notions of r-generalized fuzzy closed sets in [31, 32, 33, 34]are investigated and we give many examples for reverse. In addition, by using r-τ12-θ-gfc sets, wedefine a new fuzzy closure operator which generates a new smooth topology. Finally, generalized fuzzyθ-continuous (resp. irresolute) and fuzzy strongly θ-continuous mappings are introduced and some oftheir properties are studied

Keywords

− Smooth topology, θ-generalized fuzzy closed, generalized fuzzy closure operator, generalized fuzzy θ-continuous mapping, generalized fuzzy θ-irresolute mapping, fuzzy strongly θ- continuousmapping