Controlled Fuzzy 2-Metric Spaces: A Soft Computing Framework with Dynamic Applications

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DOI: https://doi.org/10.28924/2291-8639-24-2026-110
Published: Apr 7, 2026
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Abhishikta Das, Dipti Barman, Tarapada Bag, Hijaz Ahmad, Waleed Mohammed Abdelfattah, Osama Oqilat, Clemente Cesarano, Controlled Fuzzy 2-Metric Spaces: A Soft Computing Framework with Dynamic Applications, Int. J. Anal. Appl., 24 (2026), 110.

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Abhishikta Das, Dipti Barman, Tarapada Bag, Hijaz Ahmad, Waleed Mohammed Abdelfattah, Osama Oqilat, Clemente Cesarano

Abstract

In this article, we introduce the concept of a controlled fuzzy 2-metric space, formulated by incorporating three control functions that flexibly regulate the fuzzy distance relationships among triplets of points. This structure provides a flexible analytical tool for modeling systems influenced by uncertainty, interdependence, and approximate reasoning. We establish several fundamental properties of this structure and derive fixed-point results. To demonstrate its practical relevance, we apply the proposed framework to a dynamic market-equilibrium problem, in which agents’ interactions are governed by fuzzy relations and control-dependent adjustments. The study also discusses implications for soft computing and decision-making systems, highlighting the framework’s potential in modeling adaptive and uncertain environments.

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