f-Statistical Convergence of order $\beta $ for Sequences of Fuzzy Numbers

TL;DR

This paper introduces and extends concepts of statistical convergence and Cesàro summability of order beta for sequences of fuzzy numbers, incorporating an unbounded modulus function to generalize existing notions.

Contribution

It defines f-statistical convergence of order beta for fuzzy sequences and establishes inclusion theorems, expanding the theoretical framework in fuzzy analysis.

Findings

Introduces f-statistical convergence of order beta for fuzzy sequences.

Establishes inclusion theorems between different convergence notions.

Generalizes convergence concepts using unbounded modulus functions.

Abstract

In this paper, we extend the notions of statistically convergence of order $\beta $ and strong Ces\`{a}ro summability of order $\beta ,$ and introduce the notions $f-$statistically convergence of order $\beta $ and strong Ces\`{a}ro summability of order $\beta $ for $\beta \in \left( 0,1\right] $ with respect to an unbounded modulus function $f$ for sequences of fuzzy numbers and give some inclusion theorems.