Metric-Based Fuzzy Equivalence and Inequality Relations

This work focuses on the studying of metric-based fuzzy equivalence and inequality relations within the framework of fuzzy logic. Namely, our emphasis lies in the examination of transitive fuzzy equivalence and inequality relations, governed by the Archimedean t-norm and t-conorm, respectively. Subsequently, we study aggregation operators, which preserve the properties of initial fuzzy equivalence and inequality relations, and illustrate their construction by employing the additive generators for different t-norms and t-conorms. Our research contributes to a deeper understanding of construction of metric-based fuzzy relations and their aggregation. This knowledge holds practical implications across diverse domains, enabling effective applications in real-world scenarios.