Soft Theta-Topology Based on Many-Valued Logic

Abstract

In the present paper we introduce fuzzifying soft topology which is defined over an initial universe with a fixed set of parameters. The notions of fuzzifying soft closed sets, fuzzifying soft neighborhood system of a soft point, fuzzifying soft derived, fuzzifying soft closure and fuzzifying soft interior are introduced and their basic properties are investigated. Furthermore, we define the notions of fuzzifying soft $\theta$-neighborhood system of a soft point, fuzzifying soft $\theta$-derived, fuzzifying soft $\theta$-closure, fuzzifying soft $\theta$-interior and investigate their properties. Finally, a fuzzifying soft continuity, a fuzzifying soft strong $\theta$-continuity and fuzzifying soft $\theta$-continuity are given and some of their basic properties are studied