Hyperfuzzy and SuperHyperfuzzy Weighted Averages

Uncertainty modeling is fundamental to decision-making across diverse domains, and numerous frameworks, such as Fuzzy Sets, Rough Sets, Hesitant Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets, have been developed to capture different facets of imprecision. Among these, Hyperfuzzy Sets and their recursive generalization, SuperHyperfuzzy Sets, assign set-valued membership degrees at multiple hierarchical levels to represent uncertainty more richly. A Fuzzy Weighted Average computes a weighted mean of fuzzy numbers by applying the extension principle to their membership functions. In this paper, we extend this concept by defining the Hyperfuzzy Weighted Average and the SuperHyperfuzzy Weighted Average based on Hyperfuzzy and SuperHyperfuzzy Sets. We present formal definitions, prove key properties, such as well-definedness, reduction to classical cases, and idempotency, and illustrate their application through examples, demonstrating enhanced aggregation of multi-level uncertainty.