2025/09/26 by Nicola Fabiano, Fabiano, Nicola · 1 citation
Decision Sciences · Mathematics · Computer Science · #Fuzzy and Soft Set Theory #Fixed Point Theorems Analysis #Data Management and Algorithms
paper · pdf · doi:10.48550/arxiv.2509.22364
We prove three structural impossibility results demonstrating that fuzzy metric spaces cannot capture essential features of quantum state geometry. First, we show they cannot model destructive interference between concepts due to phase insensitivity. Second, we prove there is no distance-preserving embedding from quantum state space into any fuzzy metric space. Third, we establish that fuzzy logic cannot distinguish symmetric from antisymmetric concept combinations -- a fundamental limitation for modeling structured knowledge. These theorems collectively show that fuzzy frameworks are structurally incapable of representing intrinsic uncertainty, where quantum mechanics provides a superior, geometrically coherent alternative.