NEUTROSOPHIC MR-METRIC SPACES: THEORY, COMPACTNESS, AND APPLICATIONS IN MACHINE LEARNING

Authors

  • Abdullah Alsoboh Department of Basic and Applied Sciences, College of Applied and Health Sciences, A'Sharqiyah University
  • Abed Al-Rahman M. Malkawi Department of Mathematics, Faculty of Arts and Science, Amman Arab University
  • Ayat M. Rabaiah Department of Mathematics, Faculty of Arts and Science, Amman Arab University
  • Ala Amourah Mathematics Education Program, Faculty of Education and Arts, Sohar University
  • Abdullrahman A. Al-Maqbali Department of Basic and Applied Sciences, College of Applied and Health Sciences, A'Sharqiyah University
  • Tala Sasa Department of Mathematics, Faculty of Science, Applied Science Private University

Abstract

This paper introduces a comprehensive framework for Neutrosophic MR-Metric Spaces (NMR-MS), combining the ternary structure of MR-metrics with the uncertaintymodeling capabilities of neutrosophic logic. We establish the fundamental theoretical foun-dations, including a first-order axiomatization of NMR-MS and a detailed analysis of com-pactness properties. Our results demonstrate that while the full theory T_{NMR} is not compact, the restricted theory T_{NMR}^{K} for bounded metrics is compact and admits ultraproduct constructions satisfying Loś's Theorem. Building on this theoretical framework, we developa novel Neutrosophic Metric Learning paradigm that generalizes standard metric learningby incorporating truth, indeterminacy, and falsity memberships.

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Published

2026-05-31

Issue

Volume 31, Number 2, June 2026

Section

Articles