Foundations of (m,n)-SuperHyperFuzzy, SuperHyperNeutrosophic, and SuperHyperPlithogenic Sets

Abstract

Uncertainty modeling is fundamental to decision-making across diverse domains, and numerous frame works—such as Fuzzy Sets [1], Rough Sets [2,3], Vague Sets [4,5], Intuitionistic Fuzzy Sets [6,7], Hesitant Fuzzy Sets [8,9], Soft Sets [10,11], Neutrosophic Sets [12,13], and Plithogenic Sets [14,15]—have been developed to capture different facets of imprecision. Among these extensions are Hyperfuzzy Sets [16] and their recursive generalizations, SuperHyperfuzzy Sets [17], which assign set-valued membership degrees at multiple hierarchical levels. Similarly, corresponding hyper and superhyper extensions have been proposed for Neutrosophic and Plithogenic frameworks. These constructions enable clear, intuitive modeling of inherently hierarchical and complex uncertainties. In this paper, we review the notions of (?,?)-SuperHyperfuzzy Sets, (?,?)-SuperHyperneutrosophic Sets, and (?,?)-SuperHyperPlithogenic Sets, and illustrate their use through several concrete examples.