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

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.