TY  - JOUR
T1  - Soft Union-symmetric Difference Complement Product of Groups
AU  - Sezgin, Aslıhan
AU  - Ay, Zeynep
PY  - 2025
DA  - November
Y2  - 2025
JF  - Natural Sciences and Engineering Bulletin
JO  - NASE
PB  - Gaziantep University
WT  - DergiPark
SN  - 3023-8293
SP  - 114
EP  - 125
VL  - 2
IS  - 2
LA  - en
AB  - 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.
KW  - Sot sets
KW  - Soft subsets
KW  - Soft equalities
KW  - Soft Union-symmetric Difference Complement Product
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UR  - https://dergipark.org.tr/en/pub/nase/issue//1727506
L1  - https://dergipark.org.tr/en/download/article-file/4992046
ER  -