Soft Symmetric Difference Complement-Intersection Product of Groups

Zeynep Ay; Aslıhan Sezgin

doi:10.70030/sjmakeu.1733234

Soft Symmetric Difference Complement-Intersection Product of Groups

Abstract

Soft set theory, as a mathematically rigorous and algebraically expressive formalism, offers a powerful framework for modeling uncertainty, vagueness, and parameter-driven variability. Within this landscape, the present study introduces the soft symmetric difference complement-intersection product, a novel binary operation defined over soft sets whose parameter domains are endowed with a group-theoretic structure. Developed within a strict axiomatic foundation, the operation is proven to satisfy fundamental algebraic properties—such as closure, associativity, commutativity, and idempotency—while maintaining consistency with generalized notions of soft equality and subsethood. Its behavior is thoroughly analyzed with respect to identity and absorbing elements, as well as interactions with null and absolute soft sets, all within the constraints of group-parameterized domains. The findings confirm that the proposed operation forms a coherent and structurally robust algebraic system, thereby enriching the algebraic architecture of soft set theory. Furthermore, this work provides a foundational step toward the formulation of a generalized soft group theory, in which soft sets indexed by group-based parameters emulate classical group behaviors through abstract soft operations. The operation’s full integrability within soft inclusion hierarchies and its alignment with generalized soft equalities highlight its theoretical depth and broaden its potential applications in formal decision-making and algebraic modeling under uncertainty.

Keywords

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Details

Primary Language

English

Subjects

Fuzzy Computation

Journal Section

Research Article

Authors

Zeynep Ay
0009-0003-9324-0387
Türkiye

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

Early Pub Date

September 11, 2025

Publication Date

December 26, 2025

Submission Date

July 2, 2025

Acceptance Date

August 21, 2025

Published in Issue

Year 2025 Volume: 8 Number: 2

DOI

https://doi.org/10.70030/sjmakeu.1733234

IZ

https://izlik.org/JA86CL37AL

Cite

RIS / Bibtex

APA

Ay, Z., & Sezgin, A. (2025). Soft Symmetric Difference Complement-Intersection Product of Groups. Scientific Journal of Mehmet Akif Ersoy University, 8(2), 71-82. https://doi.org/10.70030/sjmakeu.1733234

AMA

1.Ay Z, Sezgin A. Soft Symmetric Difference Complement-Intersection Product of Groups. Techno-Science. 2025;8(2):71-82. doi:10.70030/sjmakeu.1733234

Chicago

Ay, Zeynep, and Aslıhan Sezgin. 2025. “Soft Symmetric Difference Complement-Intersection Product of Groups”. Scientific Journal of Mehmet Akif Ersoy University 8 (2): 71-82. https://doi.org/10.70030/sjmakeu.1733234.

EndNote

Ay Z, Sezgin A (December 1, 2025) Soft Symmetric Difference Complement-Intersection Product of Groups. Scientific Journal of Mehmet Akif Ersoy University 8 2 71–82.

IEEE

[1]Z. Ay and A. Sezgin, “Soft Symmetric Difference Complement-Intersection Product of Groups”, Techno-Science, vol. 8, no. 2, pp. 71–82, Dec. 2025, doi: 10.70030/sjmakeu.1733234.

ISNAD

Ay, Zeynep - Sezgin, Aslıhan. “Soft Symmetric Difference Complement-Intersection Product of Groups”. Scientific Journal of Mehmet Akif Ersoy University 8/2 (December 1, 2025): 71-82. https://doi.org/10.70030/sjmakeu.1733234.

JAMA

1.Ay Z, Sezgin A. Soft Symmetric Difference Complement-Intersection Product of Groups. Techno-Science. 2025;8:71–82.

MLA

Ay, Zeynep, and Aslıhan Sezgin. “Soft Symmetric Difference Complement-Intersection Product of Groups”. Scientific Journal of Mehmet Akif Ersoy University, vol. 8, no. 2, Dec. 2025, pp. 71-82, doi:10.70030/sjmakeu.1733234.

Vancouver

1.Zeynep Ay, Aslıhan Sezgin. Soft Symmetric Difference Complement-Intersection Product of Groups. Techno-Science. 2025 Dec. 1;8(2):71-82. doi:10.70030/sjmakeu.1733234