Soft Union-symmetric Difference Complement Product of Groups

Zeynep Ay; Aslıhan Sezgin

Soft Union-symmetric Difference Complement Product of Groups

Abstract

Soft set theory offers a logically rigorous and algebraically expressive framework for representing systems marked by ambiguity, epistemic uncertainty, and parameter-dependent variability. In this study, we introduce the soft union–symmetric difference complement product, a novel binary operation defined over soft sets whose parameter domains possess an intrinsic group-theoretic structure. Constructed within a formally consistent axiomatic framework, the operation ensures full compatibility with generalized formulations of soft subsethood and soft equality. A comprehensive algebraic analysis is conducted to establish key structural properties—closure, associativity, commutativity, and idempotency,—while also rigorously characterizing the operation’s interaction with identity, absorbing, null, and absolute soft sets. The results affirm that the proposed product satisfies all requisite algebraic constraints imposed by group-parameterized domains, thereby generating a coherent and internally robust algebraic structure over the universe of soft sets. Beyond its foundational significance, this operation enriches the operational arsenal of soft set theory and lays the groundwork for the emergence of a generalized soft group theory. Moreover, its formal alignment with core relational structures such as soft equality and inclusion underscores its applicability to a wide range of analytical domains—including abstract algebraic modeling, uncertainty-aware classification, and multi-criteria decision-making—thus offering both deep theoretical insights and tangible avenues for practical deployment.

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Zeynep Ay
0009-0003-9324-0387
Türkiye

Aslıhan Sezgin ^*
0000-0002-1519-7294
Türkiye

Publication Date

November 27, 2025

Submission Date

June 25, 2025

Acceptance Date

September 16, 2025

Published in Issue

Year 2025 Volume: 2 Number: 2

IZ

https://izlik.org/JA94MK75ZS

Cite

RIS / Bibtex

APA

Ay, Z., & Sezgin, A. (2025). Soft Union-symmetric Difference Complement Product of Groups. Natural Sciences and Engineering Bulletin, 2(2), 114-125. https://izlik.org/JA94MK75ZS

AMA

1.Ay Z, Sezgin A. Soft Union-symmetric Difference Complement Product of Groups. NASE. 2025;2(2):114-125. https://izlik.org/JA94MK75ZS

Chicago

Ay, Zeynep, and Aslıhan Sezgin. 2025. “Soft Union-Symmetric Difference Complement Product of Groups”. Natural Sciences and Engineering Bulletin 2 (2): 114-25. https://izlik.org/JA94MK75ZS.

EndNote

Ay Z, Sezgin A (November 1, 2025) Soft Union-symmetric Difference Complement Product of Groups. Natural Sciences and Engineering Bulletin 2 2 114–125.

IEEE

[1]Z. Ay and A. Sezgin, “Soft Union-symmetric Difference Complement Product of Groups”, NASE, vol. 2, no. 2, pp. 114–125, Nov. 2025, [Online]. Available: https://izlik.org/JA94MK75ZS

ISNAD

Ay, Zeynep - Sezgin, Aslıhan. “Soft Union-Symmetric Difference Complement Product of Groups”. Natural Sciences and Engineering Bulletin 2/2 (November 1, 2025): 114-125. https://izlik.org/JA94MK75ZS.

JAMA

1.Ay Z, Sezgin A. Soft Union-symmetric Difference Complement Product of Groups. NASE. 2025;2:114–125.

MLA

Ay, Zeynep, and Aslıhan Sezgin. “Soft Union-Symmetric Difference Complement Product of Groups”. Natural Sciences and Engineering Bulletin, vol. 2, no. 2, Nov. 2025, pp. 114-25, https://izlik.org/JA94MK75ZS.

Vancouver

1.Zeynep Ay, Aslıhan Sezgin. Soft Union-symmetric Difference Complement Product of Groups. NASE [Internet]. 2025 Nov. 1;2(2):114-25. Available from: https://izlik.org/JA94MK75ZS