Fuzzy soft numbers

TL;DR

This paper introduces fuzzy soft numbers, defining their arithmetic operations, properties, and related concepts like distance, convergence, and continuity within fuzzy soft metric spaces.

Contribution

It presents the novel concept of fuzzy soft numbers along with their arithmetic, properties, and foundational metric space concepts.

Findings

Defined fuzzy soft numbers and operations

Established properties and metric space concepts

Explored convex and concave fuzzy soft sets

Abstract

In this paper, we introduce the notion of fuzzy soft numbers. Here defined fuzzy soft number and four arithmetic operations $ \tilde{+}, \tilde{-}, \tilde{\times}, \tilde{\div} $ and related properties. Also introduce Hausdorff distance, Fuzzy soft metric space, convergence sequence, Cauchy sequence, Continuity, and uniform continuity of fuzzy soft numbers. At starting of this paper, we study convex and concave fuzzy soft sets and some of their properties.