Some new sets, Topologies and Decomposition of weaker forms of continuity via Fuzzy Ideals

Abstract

The purpose of this paper is to introduce fuzzy L*-perfect, fuzzy R*-perfect, fuzzy C*-perfect and fuzzy f_I -sets in fuzzy ideal topological spaces. Furthermore, we have introduced R* topology using fuzzy ideal topological spaces. The characterization for compatible ideals via fuzzy R*-perfect sets and a fuzzy topology via ideals which is finer than τ using fuzzy R* -perfect sets on a finite set is obtained. Moreover, the fuzzy weakly γ-I -open set is introduced. Some related concepts like fuzzy weakly γ-I-continuous functions, fuzzy weakly γ-I-open functions and fuzzy weakly γ-I-closed functions are also defined. The characterizations along with their properties concerning all these concepts are discussed. Finally, a new decomposition of weaker forms of fuzzy continuity is obtained using fuzzy weakly γ-I-open sets.