# Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

## TL;DR

This paper introduces new spaces of triangular fuzzy numbers within matrix domains, exploring their structural, topological, and algebraic properties to advance fuzzy set theory and its applications.

## Contribution

It constructs and analyzes novel spaces of triangular fuzzy numbers in matrix domains, expanding the mathematical framework of fuzzy set theory.

## Key findings

- New space of triangular fuzzy numbers defined within matrix domains.
- Structural, topological, and algebraic properties characterized.
- Potential applications in fuzzy modeling and uncertainty analysis.

## Abstract

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics, fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.