FUZZY METRIC SPACES: THEORY AND APPLICATIONS IN MEDICAL IMAGING, TRANSPORTATION, AND SOCIAL NETWORKS

Abstract

This paper introduces new ideas in fuzzy metric space theory, focusing on M*-metric and MR-metric spaces. We present three main theorems: (1) an embedding theoremfor fuzzy M*-metric spaces with contraction properties, (2) a fixed point theorem for fuzzy contractions in MR-metric spaces, and (3) a compatibility theorem for fuzzy metrics thatcombine M*-and MR-metric structures. We apply these results to three areas: tumorboundary detection in medical imaging, traffic ow analysis in transportation networks, andcommunity detection in social networks. Our methods show practical improvements: medical imaging achieves a Dice score of 0:89 ± 0:03, trac models converge 21% faster, and socialnetwork analysis maintains precision above 0.85. These results provide strong mathematical foundations for handling uncertainty in real-world applications.