Work

Multidimensional Topological Measure Spaces and Their Applications in Decision‐Making Problems

Year: 2026

Type: article

Abstract: This paper presents a generalized framework termed the multidimensional topological measure space (MDTMS), developed through multidimensional fuzzy sets, multidimensional topology, and an associated distance measure. The suggested framework enhances traditional fuzzy models by facilitating a more nuanced representation and examination of intricate, multiparameter data. Essential core components, including multidimensional fuzzy topology, basis, and subspace, are rigorously described within this framework. We create many mathematical instruments to facilitate study inside the MDTMS framework, encompassing concepts of multidimensional carrier, closure, core, and interior. Additionally, we analyze sequences of multidimensional fuzzy sets and introduce two forms of convergence, together with their fundamental characteristics. To illustrate the practical significance of the proposed framework, we introduce a decision‐making methodology grounded in Euclidean multidimensional distance functions incorporated within the MDTMS structure. Examples are shown to demonstrate the relevance and efficacy of the proposed notions.

Source: Advances in Fuzzy Systems

DOI: 10.1155/adfs/7832893

Authors: Jomal Josen, Sunil Jacob John, T. Baiju

Institutions: St. Thomas College (Autonomous), National Institute of Technology Calicut, Manipal Academy of Higher Education

Language: English

Topic: Fuzzy and Soft Set Theory

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,000

Funders: Department of Science and Technology, Ministry of Science and Technology, India, University Grants Commission