HyperFuzzy and SuperHyperFuzzy Group Decision-Making

Abstract

Fuzzy sets capture vagueness by assigning each element a membership value in[0,1][1, 2]. Hyperfuzzy setsextend this idea by mapping each element to a nonempty subset of[0,1], thereby encoding both uncertainty andvariability in membership degrees [3–5]. An(m,n)-superhyperfuzzy set further generalizes these notions byassigning to each nonempty member of themth andnth iterated powersets a nonempty family of subsets of[0,1],enabling the representation of hierarchical and nested imprecision [6]. Fuzzy group decision making aggregatesexperts’ fuzzy preference relations to produce collective rankings or to select optimal alternatives [7–9].Despite the considerable importance of fuzzy group decision making, corresponding frameworks for hyper-fuzzy and superhyperfuzzy sets remain unexplored. In this paper, we introduce Hyperfuzzy and(m,n)-SuperHyperfuzzy Group Decision Making frameworks: we define new aggregation operators and decisionrules, and we illustrate their ability to accommodate richer forms of uncertainty with detailed examples.