Score and Distance Measures in Q-Complex Fermatean Neutrosophic Set Theory

Abstract

Q-complex neutrosophic sets (Q-CNS) and Q-complex Fermatean neutrosophic sets (Q-CFNS) represent recent extensions of fuzzy set theory that introduce complex-valued membership degrees to better capture ambiguity. Q CNS builds on neutrosophic sets by expressing the truth, indeterminacy, and falsity components as complex numbers, allowing for richer and more flexible representation of uncertainty. Q-CFNS advances this framework further by adopting Fermatean-type membership grades, which offer improved precision in capturing imprecise information. This added structure supports more nuanced applications across decision-making, artificial intelligence, and data analysis, allowing complex relationships and vague data to be modeled with greater fidelity. In essence, these are complex-valued sets governed by Fermatean-type constraints, designed to comprehensively handle multiple dimensions of uncertainty. Their strength becomes particularly evident in situations where conventional fuzzy sets fall short — for instance, when dealing with inconsistent or partially missing data. By leveraging Q-CNS and Q-CFNS, researchers and practitioners gain a more robust toolset for modeling complex real-world systems. In this article, we introduce and define score and distance functions specifically for Q-CFNS.