Foundations and framework of superhypersoft sets

Abstract

Superhypersoft sets (SHSS) represent an advanced extension of soft sets and hypersoft sets,  designed to address complex multi-parameterized decision-making problems in uncertain environments. This  study explores the foundational theories of soft set and hypersoft set models, leading to the formulation of  SHSS as a more generalized and flexible framework for managing intricate data structures. We define key  operations and properties of SHSS and establish their basic algebraic laws. The findings show that SHSS  improves the mathematical abilities of existing soft set models by adding more structural complexity, which  makes them suitable for complicated classification and decision-support systems. Even with such potential,  SHSS is still a relatively new field with many undiscovered research possibilities, such as formalization of  basic operations, discussion of basic algebraic laws, algorithmic implementations and real-world applications  in different fields. This study inspires more developments in soft set theory and uncertainty modeling by  establishing the foundation for future research into the theoretical and applied aspects of SHSS.