A Study on Hyperfuzzy Hyperrough Sets, Hyperneutrosophic Hyperrough Sets, and Hypersoft Hyperrough Sets with Applications in Cybersecurity

Abstract

Rough Sets approximate subsets by defining lower and upper bounds, effectively capturing uncertainty through equivalence classes or indiscernibility relations. Additionally, concepts such as Fuzzy Sets, Neutrosophic Sets, and Soft Sets are well-known for addressing uncertainty, with numerous applications explored in various fields. This paper extends these foundational concepts by introducing six advanced frameworks: the Hyperfuzzy Rough Set, Hyperfuzzy Hyperrough Set, HyperNeutrosophic Rough Set, HyperNeutrosophic Hyperrough Set, Hypersoft Hyperrough Set, and Multigranulation Hyperrough Set. These new models aim to enhance the theoretical understanding and practical handling of uncertainty.