Some Properties of Gradation of Openness of Soft Sets

The purpose of the current work is to analyze the fundamental behaviours of gradation of openness of soft sets, a new approach of fuzzy soft topological space, where the underlying topology is a gradation of openness of soft sets using soft elements and elementary soft operations. For this, firstly, for any real number r \in \left[۰,۱ \right], the r-level neighbourhood system of a soft element, r-level interior, r-level open, r-level closed of a soft set etc. are defined, their basic properties and relationships including celebrated decomposition theorems are studied. Further to test continuity, openness, closedness of a soft mapping, the definitions of sgp-map, FS-open map, FS-homeomorphism are mentioned and their features are explored. Finally, subspace gradation of openness is commenced and some of their properties are discussed.

کلیدواژه ها:

Soft element ، Soft mapping ، Soft topology ، Gradation of openness ، Fuzzy soft topology