Some characterizations on weighted $\alpha\beta$-statistical convergence of fuzzy functions of order $\theta$

TL;DR

This paper introduces a new type of weighted $eta$-statistical convergence of fuzzy functions of order $ heta$, analyzing its properties and relationships, and examining how classical function properties are preserved under this convergence.

Contribution

It extends the concept of statistical convergence to fuzzy functions with weights and order, classifies different modes, and explores their properties and interrelations.

Findings

Weighted $eta$-statistical convergence of fuzzy functions is classified into pointwise, uniform, and equi-statistical modes.

Continuity and boundedness are preserved under equi-statistical convergence but not necessarily under pointwise convergence.

Basic properties and relationships among different convergence modes are established.

Abstract

Based on the concept of new type of statistical convergence defined by Aktuglu, we have introduced the weighted $\alpha\beta$ - statistical convergence of order $\theta$ in case of fuzzy functions and classified it into pointwise, uniform and equi-statistical convergence. We have checked some basic properties and then the convergence are investigated in terms of their $\alpha$-cuts. The interrelation among them are also established. We have also proved that continuity, boundedness etc are preserved in the equi-statistical sense under some suitable conditions, but not in pointwise sense.