Extensions of fuzzy soft sets and rings

Abstract

In this note, first we introduce the concept of extension of fuzzy soft subset (set) by utilizing its extension of mapping and re-define some operations of fuzzy soft sets based on the extension. Furthermore, we also discuss the extension of fuzzy soft set with respect to t-level soft sets of fuzzy soft sets. We explore the connection between both types of the extensions in example4.1. As an evidence we present the extension of fuzzy soft subrings and fuzzy soft ideals while considering the extension through t-level soft sets.