On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies

Abstract

In this work, we introduce the concepts of r-fuzzy soft δ-open (resp. semi-open and α-open) sets on fuzzy soft topological space, the relations of these sets with each other are established. Next, we introduce the concepts of fuzzy soft δ-continuous (resp. β-continuous, semi-continuous, pre-continuous and α-continuous) functions, and some properties of these functions along with their mutual relationships are investigated. Also, a decomposition of fuzzy soft semi-continuity and a decomposition of fuzzy soft α-continuity are given. Finally, as a weaker form of fuzzy soft continuity by Aygunoglu et al. (2014), the concepts of fuzzy soft almost (resp. weakly) continuous functions are introduced, and some properties are specified. Moreover, we explore the notion of continuity in a very general setting namely fuzzy soft (L, M, N, O)-continuous functions, and a historical justification are obtained.