Harnessing Quantum Superposition in Soft Set Theory: Introducing Quantum Hypersoft and SuperHyperSoft Sets

Abstract

This paper presents two novel extensions of the Quantum Soft Set framework by integrating the hierarchical structures of hypersoft and superhypersoft sets with quantum superposition principles. Soft sets offer a versatile approach to decision making by associating parameters with subsets of a universal set, effectively capturing uncertainty and imprecision. Hypersoft and superhypersoft sets further generalize this paradigm for increasingly complex scenarios. A Quantum Soft Set maps each parameter to a normalized quantum state, enabling probabilistic membership via amplitude coefficients. We rigorously define the Quantum Hypersoft Set and the Quantum SuperHypersoft Set, laying a foundation for future advances in quantum‐enhanced decision analysis, topological modeling, and algebraic applications.