Soft symmetric difference complement-plus product of groups

Authors

https://doi.org/10.48313/uda.v3i1.94

Abstract

Soft set theory offers a robust framework for representing systems characterized by uncertainty, ambiguity, and parameter-driven variability features often present in complex decision-making and information processing. Within this context, the current study introduces the soft symmetric difference complement–plus product, a distinct binary operation defined on soft sets whose parameter domains are structured according to group-theoretic principles. This operation is rigorously formulated within an axiomatic framework and is shown to be fully compatible with extended forms of soft equality and subsethood. Through detailed algebraic analysis, the paper demonstrates that the operation satisfies essential properties such as closure, associativity, commutativity, and idempotency. It also explores the operation’s interaction with identity and absorbing elements, as well as with null and absolute soft sets—under the structural constraints of group-parameterized domains. The findings confirm that the proposed operation aligns with group-theoretic axioms and establishes a coherent algebraic system within soft set theory. Beyond its foundational role, the operation paves the way for a generalized form of soft group theory, where classical group behaviors are replicated in soft sets indexed by group-based parameters using abstract soft-defined operations. Its consistency with generalized notions of soft equality and hierarchical soft subset structures further underscores its theoretical richness. Overall, the study provides a significant algebraic contribution and lays the groundwork for extending soft set theory to applications requiring formal reasoning under uncertainty, abstract algebraic modeling, and multi-criteria analysis.

Keywords:

Soft sets, Soft subsets, Soft equalities, Soft symmetric difference complement-plus

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Published

2026-03-06

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Vol. 3 No. 1 (2026): Uncertainty Discourse and Applications

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Articles

How to Cite

Ay, Z., & Sezgin, A. (2026). Soft symmetric difference complement-plus product of groups. Uncertainty Discourse and Applications, 3(1), 1-13. https://doi.org/10.48313/uda.v3i1.94

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