The paper concludes by introducing the concept of soft subdirings and exploring their structural aspects in detail.
📌 3 Key Takeaways
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Objective & Hypothesis:This paper proposes the notion of soft dirings, created by combining soft set theory with dirings structure, which are an extension of as a generalization of rings.
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Key Findings & Data:It investigates several properties of soft dirings and includes examples to clarify these concepts.
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Conclusion & Impact:The paper concludes by introducing the concept of soft subdirings and exploring their structural aspects in detail.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Soft set · Diring · Subdiring
Abstract
This paper proposes the notion of soft dirings, created by combining soft set theory with dirings structure, which are an extension of as a generalization of rings. It investigates several properties of soft dirings and includes examples to clarify these concepts. The concept of commutative soft dirings is defined. In addition, a categorical framework for soft dirings and commutative soft dirings is presented. The paper concludes by introducing the concept of soft subdirings and exploring their structural aspects in detail.
Oğuz, G. (2025). On Characterizations of Soft Dirings. Turkish Journal of Mathematics and Computer Science, Volume: 17 Issue: 2. https://doi.org/10.47000/tjmcs.1716605
Abbasi, M.Y., Mir, T.R., Khan S.A., Characteristics of Soft Fractional Ideals and its R-multiples of Integral Domains, Palestine Journal of Mathematics, 13(3)(2024), 392–399.
Acar, U., Koyuncu, F., Tanay, B., Soft sets and soft rings, Computers and Mathematics with Applications, 59(11)(2010), 3458–3463.
Adhikari, M.R., Adhikari A., Groups, Rings and Modules with Applications, Universities Press, 2003.
Ghosh, S.K., Mitra, A., Ghosh, A., A novel intuitionistic fuzzy soft set entrenched mammogram segmentation under multigranulation approximation for breast cancer detection in early stages, Expert Systems with Applications, 169(2021), 114329.
Kazanci, O., Yilmaz, S., Yamak, S., Soft sets and soft BCH-algebras, Hacet. J. Math. Stat., 39(2010), 205–217.
Kelarev, A.V., Ring constructions and applications., World Scientific,9(2002).
Khalil, A.M., Li, S.G., Lin, Y., Li, H.X., Ma, S.G., A new expert system in prediction of lung cancer disease based on fuzzy soft sets, Soft Computing, 24(18)(2020), 14179–14207.
Maji, P.K., Roy, A.R., Biswas, R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44(2002), 1077–1083.
Maji, P.K., Biswas, R., Roy, A.R., Soft set theory, Comput. Math. Appl., 45(4–5)(2003), 555–562.
Oguz, G., Davvaz, B., Soft topological hyperstructure, Journal of Intelligent and Fuzzy Systems, 40(5)(2021), 8755–8764.
Sezgin, A., Atagün, A.O., On operations of soft sets, Computers and mathematics with applications, 61(5)(2011), 1457–1467.
Shah, T., Shaheen, S., Soft topological groups and rings, Ann. Fuzzy Math. Inform, 7(5)(2014), 725–743.
Sun, Q.M., Zhang, Z.L., Liu, J., Soft sets and soft modules, In Rough Sets and Knowledge Technology: Third International Conference. Chengdu, China, Springer Berlin Heidelberg, 3(2008), 403–409.
Tasbozan, H., Icen, I., Bagirmaz, N., Ozcan, A.F., Soft sets and soft topology on nearness approximation spaces, Filomat, 31(13)(2017), 4117–4125.
Zahedi Khameneh, A., Kılıc¸man, A., Multi-attribute decision-making based on soft set theory: A systematic review, Soft Computing, 23(2019), 6899–6920.
Zou, Y., Xiao, Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21(8)(2008), 941–945.