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

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 (𝑚,𝑛)-SuperHyperfuzzy Sets, (𝑚,𝑛)-SuperHyperneutrosophic Sets, and (𝑚,𝑛)-SuperHyperPlithogenic Sets, and illustrate their use through several concrete examples.