Soft Intersection-gamma Product of Groups

Abstract

Soft set theory provides a logical and expressive algebraic framework for modeling systems with ambiguity, uncertainty, and parameter-dependent variability. In this study, we introduce the soft intersection-gamma product, a new binary operation on soft sets with group-theoretic structure in their parameter domains. Formally described within an axiomatic framework, the operation is fully compatible with expanded notions of soft equality and soft subsethood. In addition to its behavior with respect to identity, absorbing, null, and absolute soft sets, important structural features like closure, associativity, commutativity, idempotency, and distributivity are thoroughly examined algebraically. The results show that the operation satisfies all algebraic constraints imposed by group-indexed domains and constructs a robust and coherent algebraic system on the universe of soft sets. Apart from its theoretical significance, the operation strengthens the algebraic foundation of soft set theory and offers a solid foundation for a generalized soft group theory. Moreover, its formal coherence with soft subset and equality relations enhances its utility in areas like as classification, decision-making, and uncertainty-aware modeling, offering substantial potential for both abstract theoretical development and practical implementations.