Some Results on Statistically Pre-Cauchy Sequences of Fuzzy Variables Defined by Orlicz Functions in Credibility Space

Abstract

This study introduces the concept of statistically pre-Cauchy sequences of fuzzy variables in five directions of credibility theory: almost surely, in measure, in mean, in distribution, and uniformly almost surely. However, the main focus is kept on statistically pre-Cauchy sequences in measure, in mean, and in distribution. Furthermore, a correlation between statistically pre-Cauchy sequences and statistically convergent sequences is established using fuzzy variables. Additionally, the exploration of statistically pre-Cauchy sequences of fuzzy variables is initiated through the application of Orlicz functions. The objective is to enhance the understanding of the statistical behavior and convergence properties of fuzzy variables in various credibility scenarios. © 2024 Elsevier B.V., All rights reserved.