A Study of Sequence Spaces Defined by Statistical Convergence of Fuzzy Numbers

Abstract

Sequence spaces are mathematical structures that play a pivotal role in studying functional analysis, topology, and sequence theory. These spaces consist of sequences of elements from a given set, typically the set of real or complex numbers, equipped with
specific topological or algebraic properties. It explores sequence spaces defined by the statistical convergence of fuzzy numbers, focusing on the development and analysis of new sequence spaces that extend classical sequence spaces in the context of fuzzy
set theory. Employing a difference operator, furthermore, provides a sequence space of fuzzy numbers, F _(c) I (S) and F_(c) I (S)₀, determined via I-statistical convergence. Research investigates the basic algebraic and topological features of these spaces, offering a
thorough examination of their structural features. Additionally, it explores crucial links related to these spaces, including symmetry, solidity, and convergence-free features, and it establishes several significant inclusion outcomes. The research advances knowledge
of I-statistical convergence in fuzzy number sequence space by expanding on traditional ideas and providing guidance on using them in fuzzy set theory and uncertainty-related fields.