Uncertainty modeling underpins decision-making in many domains. Over the years, numerous frameworks have been proposed to capture different facets of imprecision, including fuzzy sets 1, 2, rough sets 3, 4, hesitant fuzzy sets 5, 6, neutrosophic sets 7, 8, and plithogenic sets 9, 10. More recently, hyperfuzzy sets and their recursive generalization, superhyperfuzzy sets, have been introduced to assign set-valued membership degrees at multiple hierarchical levels, thereby enriching the representation of uncertainty 11,12. In parallel, a variety of fuzzy-number extensions—triangular, trapezoidal, pentagonal, hexagonal, and octagonal fuzzy numbers—together with ranking functions on fuzzy numbers, have been studied and applied in decisionmaking and related fields 13, 14. In this paper, we develop hyperfuzzy and superhyperfuzzy analogues of these fuzzy-number constructs. Our aim is to provide a unified, hierarchically structured toolkit for modeling complex uncertainty in decision support and beyond.
Tsunenori Fujita (Mon,) studied this question.