Soft Union-symmetric Difference Complement Product of Groups

Zeynep Ay; Aslıhan Sezgin

Soft Union-symmetric Difference Complement Product of Groups

Öz

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.

Anahtar Kelimeler

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Temel Matematik (Diğer)

Bölüm

Araştırma Makalesi

Yazarlar

Zeynep Ay
0009-0003-9324-0387
Türkiye

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

Yayımlanma Tarihi

27 Kasım 2025

Gönderilme Tarihi

25 Haziran 2025

Kabul Tarihi

16 Eylül 2025

Yayımlandığı Sayı

Yıl 2025 Cilt: 2 Sayı: 2

IZ

https://izlik.org/JA94MK75ZS

Kaynak Göster

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, ve 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 (01 Kasım 2025) Soft Union-symmetric Difference Complement Product of Groups. Natural Sciences and Engineering Bulletin 2 2 114–125.

IEEE

[1]Z. Ay ve A. Sezgin, “Soft Union-symmetric Difference Complement Product of Groups”, NASE, c. 2, sy 2, ss. 114–125, Kas. 2025, [çevrimiçi]. Erişim adresi: https://izlik.org/JA94MK75ZS

ISNAD

Ay, Zeynep - Sezgin, Aslıhan. “Soft Union-symmetric Difference Complement Product of Groups”. Natural Sciences and Engineering Bulletin 2/2 (01 Kasım 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, ve Aslıhan Sezgin. “Soft Union-symmetric Difference Complement Product of Groups”. Natural Sciences and Engineering Bulletin, c. 2, sy 2, Kasım 2025, ss. 114-25, https://izlik.org/JA94MK75ZS.

Vancouver

1.Zeynep Ay, Aslıhan Sezgin. Soft Union-symmetric Difference Complement Product of Groups. NASE [Internet]. 01 Kasım 2025;2(2):114-25. Erişim adresi: https://izlik.org/JA94MK75ZS