A Detailed Investigation on Soft Intersection-union Product of Groups
TOTAL VIEWS: 2505
Abstract
Soft set theory provides a highly adaptable mathematical framework for address-ing real-world problems involving uncertainty, ambiguity, and parameter-driven variability—features commonly encountered in fields such as decision science, engineering, economics, and information systems. At the heart of this theory lie the fundamental operations and product constructions on soft sets, which together form a rich algebraic infrastructure capable of addressing complex, parame-ter-dependent phenomena. Accordingly, this study begins with a rigorous examina-tion of the intersection operation of soft sets. This study rigorously analyzes the intersection operation of soft sets, proving that they form a bounded semilattice in the collection of soft sets with a fixed parameter set. We then introduce the soft intersection-union product, demonstrating its hemiring structure in the mentioned collection. Key results include associativity (Proposition 4.5), non-commutativity in non-abelian groups (Proposition 4.7), and distributivity over intersection (Proposi-tion 4.24 and Proposition 4.25). The proposed algebraic constructions not only enrich the theoretical underpinnings of soft set theory but also offer promising tools for developing soft computational models applicable to multi-criteria deci-sion-making, group-based classification, and uncertainty-aware data analysis.
Keywords
Soft sets; Soft subsets; Soft equalities; Soft intersection-union product
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How to cite this paper
A
Detailed Investigation on Soft Intersection-union Product of Groups
How to
cite this paper: Aslıhan Sezgin, İbrahim Durak.
(2025) A Detailed Investigation on Soft Intersection-union Product of Groups International
Journal of Statistics and Data Science, 1(1), 7-18.
http://dx.doi.org/10.26855/ijsds.2025.12.002
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