HyperFuzzy and SuperHyperFuzzy Group Decision-Making

Takaaki Fujita

doi:10.31181/sdmap4158

Authors

Takaaki Fujita Independent Researcher, Shinjuku, Tokyo, Japan Author https://orcid.org/0000-0002-9380-386X

DOI:

https://doi.org/10.31181/sdmap4158

Keywords:

Fuzzy Set, Group Decision-Making, Fuzzy Group Decision-Making, HyperFuzzy Group Decision-Making, SuperHyperFuzzy Group Decision-Making

Abstract

Fuzzy sets model vagueness by assigning each element a membership value in the interval [0,1].
Hyperfuzzy sets extend this concept by mapping each element to a nonempty subset of [0,1], thereby capturing both uncertainty and variability in membership degrees. An (m,n)-superhyperfuzzy set further generalizes these ideas by associating each nonempty element of the mth and nth iterated powersets with a nonempty family of subsets of [0,1], enabling the representation of hierarchical and nested forms of imprecision. Decision-making refers to the process of identifying, evaluating, and selecting the most suitable option from multiple alternatives to achieve specified objectives. Fuzzy group decision-making aggregates experts’ fuzzy preference relations to produce collective rankings or to select optimal alternatives. While extensive research has been conducted on hyperfuzzy and superhyperfuzzy sets as well as on fuzzy group decision-making, their integrated framework remains largely unexplored. Motivated by this gap, the present study investigates the formulation, properties, and potential applications of hyperfuzzy and superhyperfuzzy group decision-making.

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