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Journals / International Journal of Innovative Research and Reviews / 2025 / Volume: 9 Issue: 2

Soft Intersection-gamma Product of Groups

Zeynep Ay(AMASYA UNIVERSITY)0009-0003-9324-0387
Aslıhan Sezgin(AMASYA UNIVERSITY)0000-0002-1519-7294
Pages
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Publication Date
2025-12-15
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results demonstrate that the operation satisfies all algebraic constraints of group-indexed domains, thereby forming a robust and coherent algebraic system on the universe of soft sets.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Soft set theory offers an algebraic framework for modeling systems characterized by ambiguity, uncertainty, and parameter-dependent variability.
📊
Key Findings & Data:The results demonstrate that the operation satisfies all algebraic constraints of group-indexed domains, thereby forming a robust and coherent algebraic system on the universe of soft sets.
💡
Conclusion & Impact:These connections highlight its potential for both theoretical development and practical use
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Soft sets · Soft subsets · Soft equalities

Abstract

Soft set theory offers an algebraic framework for modeling systems characterized by ambiguity, uncertainty, and parameter-dependent variability. This study introduces the soft intersection–gamma product, a new binary operation on soft sets whose parameter domains follow a group-theoretic structure. The operation is defined axiomatically and shown to be fully compatible with extended notions of soft equality and soft subsethood. We also examine the operation with respect to identity, absorbing, null, and absolute soft sets. Its structural properties, including closure, associativity, commutativity, idempotency, and distributivity, are studied in detail. The results demonstrate that the operation satisfies all algebraic constraints of group-indexed domains, thereby forming a robust and coherent algebraic system on the universe of soft sets. Beyond its theoretical significance, the operation reinforces the algebraic basis of soft set theory and provides a framework for developing a generalized soft group theory.Furthermore, its coherence with soft subset and equality relations increases its applicability in classification, decision-making, and uncertainty-aware modeling. These connections highlight its potential for both theoretical development and practical use

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Cite This Article

Ay, Z., Sezgin, A. (2025). Soft Intersection-gamma Product of Groups. International Journal of Innovative Research and Reviews, Volume: 9 Issue: 2. https://ajindex.com/articles/1496383

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