Restricted and extended plus operations for soft sets
Soft set theory has gained importance as an innovative approach for addressing uncertainty-related problems and modeling uncertainty since it was introduced by Molodtsov in 1999. It has several applications in both theoretical and practical contexts. Soft set operations, the basic concept of the the...
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| Language: | English |
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REA Press
2025-03-01
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| Series: | Computational Algorithms and Numerical Dimensions |
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| Online Access: | https://www.journal-cand.com/article_203869_e56965f5c02fe9ab4baacb7a21ea64b9.pdf |
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| author | Aslıhan Sezgin Fitnat Aybek Nurcan Güngör |
| author_facet | Aslıhan Sezgin Fitnat Aybek Nurcan Güngör |
| author_sort | Aslıhan Sezgin |
| collection | DOAJ |
| description | Soft set theory has gained importance as an innovative approach for addressing uncertainty-related problems and modeling uncertainty since it was introduced by Molodtsov in 1999. It has several applications in both theoretical and practical contexts. Soft set operations, the basic concept of the theory, have been of interest to researchers since the theory's inception, and some restricted and extended soft set operations have been defined and studied with their properties. This paper introduces a new restricted and extended soft set operation, which we refer to as restricted plus and extended plus operations. We also analyze these operations' fundamental algebraic characteristics in depth. Additionally, these operations' distributions over several soft-set operations are examined. By considering the algebraic properties of the operation and its distribution rules, we show that extended plus operation and other types of soft sets form many important algebraic structures, including semiring and near semiring in the collection of soft sets over the universe. Since the primary notion of the theory is the operations of soft sets as they serve not only the decision-making processes as accurately as possible but also the foundation for various applications, including cryptology, this theoretical study is of great importance both theoretically and practically. |
| format | Article |
| id | doaj-art-5f2f1306b1b34e748e7a126e248befd2 |
| institution | Kabale University |
| issn | 2980-7646 2980-9320 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | REA Press |
| record_format | Article |
| series | Computational Algorithms and Numerical Dimensions |
| spelling | doaj-art-5f2f1306b1b34e748e7a126e248befd22025-01-30T11:24:23ZengREA PressComputational Algorithms and Numerical Dimensions2980-76462980-93202025-03-0141659410.22105/cand.2024.475779.1107203869Restricted and extended plus operations for soft setsAslıhan Sezgin0Fitnat Aybek1Nurcan Güngör2Department of Mathematics and Science Education, Faculty of Education, Amasya University, Amasya, Türkiye.Department of Mathematics, Graduate School of Natural and Applied Sciences, Amasya University, Amasya, Türkiye.Department of Mathematics, Faculty of Arts and Science, Amasya University, Amasya, Türkiye.Soft set theory has gained importance as an innovative approach for addressing uncertainty-related problems and modeling uncertainty since it was introduced by Molodtsov in 1999. It has several applications in both theoretical and practical contexts. Soft set operations, the basic concept of the theory, have been of interest to researchers since the theory's inception, and some restricted and extended soft set operations have been defined and studied with their properties. This paper introduces a new restricted and extended soft set operation, which we refer to as restricted plus and extended plus operations. We also analyze these operations' fundamental algebraic characteristics in depth. Additionally, these operations' distributions over several soft-set operations are examined. By considering the algebraic properties of the operation and its distribution rules, we show that extended plus operation and other types of soft sets form many important algebraic structures, including semiring and near semiring in the collection of soft sets over the universe. Since the primary notion of the theory is the operations of soft sets as they serve not only the decision-making processes as accurately as possible but also the foundation for various applications, including cryptology, this theoretical study is of great importance both theoretically and practically.https://www.journal-cand.com/article_203869_e56965f5c02fe9ab4baacb7a21ea64b9.pdfsoft setssoft set operationsrestricted plus operationextended plus operation |
| spellingShingle | Aslıhan Sezgin Fitnat Aybek Nurcan Güngör Restricted and extended plus operations for soft sets Computational Algorithms and Numerical Dimensions soft sets soft set operations restricted plus operation extended plus operation |
| title | Restricted and extended plus operations for soft sets |
| title_full | Restricted and extended plus operations for soft sets |
| title_fullStr | Restricted and extended plus operations for soft sets |
| title_full_unstemmed | Restricted and extended plus operations for soft sets |
| title_short | Restricted and extended plus operations for soft sets |
| title_sort | restricted and extended plus operations for soft sets |
| topic | soft sets soft set operations restricted plus operation extended plus operation |
| url | https://www.journal-cand.com/article_203869_e56965f5c02fe9ab4baacb7a21ea64b9.pdf |
| work_keys_str_mv | AT aslıhansezgin restrictedandextendedplusoperationsforsoftsets AT fitnataybek restrictedandextendedplusoperationsforsoftsets AT nurcangungor restrictedandextendedplusoperationsforsoftsets |