A weak law of large numbers for the sequence of uncorrelated fuzzy random variables

TL;DR

This paper extends the weak law of large numbers to uncorrelated fuzzy random variables using the uniform Hausdorff metric, broadening the applicability beyond independent variables.

Contribution

It introduces a weak law of large numbers for uncorrelated fuzzy random variables, generalizing previous results for independent variables.

Findings

Proves a weak law of large numbers for uncorrelated fuzzy random variables.

Uses the uniform Hausdorff metric for convergence analysis.

Extends classical results to a broader class of fuzzy variables.

Abstract

We shall prove a weak law of large numbers for the uncorrelated (see Definition 3.1) fuzzy random variable sequence with respect to the uniform Hausdorff metric $d_H^{\infty}$, which is an extension of weak law of large numbers for independent fuzzy random variables.