Weak HyperFuzzy Set and Weak SuperHyperFuzzy Set

Abstract

Set-theoretic approaches such as fuzzy sets, neutrosophic sets, plithogenic sets, rough sets, and soft sets have proven effective for modeling uncertainty. These frameworks have been enriched by hyperstructures—based on ordinary powersets—and superhyperstructures—based on ?-fold iterated powersets—yielding the classes of HyperUncertain Sets and SuperHyperUncertain Sets [1, 2]. In this work, we introduce four new extensions: the Weak HyperFuzzy Set, the Weak HyperNeutrosophic Set, the Weak SuperHyperFuzzy Set, and the Weak SuperHyperNeutrosophic Set. Each is defined within the algebraic frameworks of Weak HyperStructure and Weak SuperHyperStructure, thereby generalizing existing HyperUncertain and SuperHyperUncertain Set theories. We present precise definitions and discuss how these weak variants enhance the expressive power for modeling hierarchical and component-wise uncertainty.