Certain properties of bounded variation of sequences of fuzzy numbers by using generalized weighted mean

TL;DR

This paper explores properties of bounded variation in sequences of fuzzy numbers using generalized weighted mean matrices, establishing relations with classical sequence classes and examining concepts like equivalence and symmetry within this framework.

Contribution

It introduces new insights into the bounded variation of fuzzy number sequences via generalized weighted means and relates these to classical sequence spaces.

Findings

Established relations between bounded variation fuzzy sequences and classical sequence classes

Analyzed concepts of equivalence and symmetry in fuzzy sequences within the new framework

Extended the understanding of fuzzy number sequence properties using generalized weighted means

Abstract

The class of bounded variation $bv^F(u,v)$ of fuzzy numbers introduced by [8] has been investigated further with the help of the generalized weighted mean matrix $G(u,v)$. Imposing some restrictions on the matrix $G(u,v)$, we have established it's relation with different class of sequences such as our known classical sets, set of all statistically null difference sequences, Cesaro sequences etc. Also we have examined the concepts like equivalent fuzzy number, symmetric fuzzy number on this quasilinear space.