Fuzzy Soft normed space and Fuzzy Soft linear operator

TL;DR

This paper introduces the concept of fuzzy soft normed spaces and fuzzy soft linear operators, exploring their properties, topological relationships, and continuity within fuzzy soft set theory.

Contribution

It is the first to define fuzzy soft normed spaces and fuzzy soft linear operators, analyzing their properties and topological connections.

Findings

Fuzzy soft normed spaces have specific properties studied.

Fuzzy soft topology relates to general topology.

Continuity of fuzzy soft linear operators is established.

Abstract

The concept of fuzzy soft set was introduced for the first time by Maji et al. in 2002, and was considered sharply from applicable aspects to theoretical aspects by a wide range of researchers. In this paper the concept of fuzzy soft norm over fuzzy soft spaces has been considered and some properties of fuzzy soft normed spaces are studied. We also study the fuzzy soft topology over a crisp set by using the fuzzy soft subsets of it and the relationship between fuzzy soft topology and general topology is investigated. Fuzzy soft linear operator over fuzzy soft spaces is introduced and continuity of such operators is considered.