New restricted and extended soft set operations: restricted gamma and extended gamma operations
Soft set theory has been well-known as an innovative approach to managing uncertainty-related problems and modelling uncertainty since Molodtsov introduced it in 1999. It has been applied in a variety of contexts, both theoretical and practical. The core concept of the theory, soft set operations, h...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
REA Press
2024-12-01
|
| Series: | Big Data and Computing Visions |
| Subjects: | |
| Online Access: | https://www.bidacv.com/article_205693_e21f87e355bde6a5826911c6b449a344.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832579288012947456 |
|---|---|
| author | Aslıhan Sezgin Fitnat Aybek |
| author_facet | Aslıhan Sezgin Fitnat Aybek |
| author_sort | Aslıhan Sezgin |
| collection | DOAJ |
| description | Soft set theory has been well-known as an innovative approach to managing uncertainty-related problems and modelling uncertainty since Molodtsov introduced it in 1999. It has been applied in a variety of contexts, both theoretical and practical. The core concept of the theory, soft set operations, has piqued the curiosity of researchers ever since it was developed. A number of restricted and extended soft set operations have been defined, and their characteristics have been investigated. In this study, we present a new restricted and extended soft set operation, which we refer to as extended gamma and restricted gamma operation, and we study their fundamental algebraic properties in detail. Additionally, this operation's distributions over other soft-set operations are examined. Considering the algebraic properties of the extended gamma operation and its distribution rules, we show that when combined with other types of soft sets, it forms several important algebraic structures, like semirings and nearsemirings, in the collection of soft sets over the universe. This theoretical study is highly significant from both a theoretical and practical standpoint, as the main notion of the theory is the operations of soft sets, which provide the basis for many applications, such as cryptology and optimal decision-making procedures. |
| format | Article |
| id | doaj-art-305daff58ad0416bb0f85c03e71c9088 |
| institution | Kabale University |
| issn | 2783-4956 2821-014X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | REA Press |
| record_format | Article |
| series | Big Data and Computing Visions |
| spelling | doaj-art-305daff58ad0416bb0f85c03e71c90882025-01-30T12:23:43ZengREA PressBig Data and Computing Visions2783-49562821-014X2024-12-014427230610.22105/bdcv.2024.478983.1199205693New restricted and extended soft set operations: restricted gamma and extended gamma operationsAslıhan Sezgin0Fitnat Aybek1Department 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.Soft set theory has been well-known as an innovative approach to managing uncertainty-related problems and modelling uncertainty since Molodtsov introduced it in 1999. It has been applied in a variety of contexts, both theoretical and practical. The core concept of the theory, soft set operations, has piqued the curiosity of researchers ever since it was developed. A number of restricted and extended soft set operations have been defined, and their characteristics have been investigated. In this study, we present a new restricted and extended soft set operation, which we refer to as extended gamma and restricted gamma operation, and we study their fundamental algebraic properties in detail. Additionally, this operation's distributions over other soft-set operations are examined. Considering the algebraic properties of the extended gamma operation and its distribution rules, we show that when combined with other types of soft sets, it forms several important algebraic structures, like semirings and nearsemirings, in the collection of soft sets over the universe. This theoretical study is highly significant from both a theoretical and practical standpoint, as the main notion of the theory is the operations of soft sets, which provide the basis for many applications, such as cryptology and optimal decision-making procedures.https://www.bidacv.com/article_205693_e21f87e355bde6a5826911c6b449a344.pdfsoft setssoft set operationsrestricted gamma operationextended gamma operation |
| spellingShingle | Aslıhan Sezgin Fitnat Aybek New restricted and extended soft set operations: restricted gamma and extended gamma operations Big Data and Computing Visions soft sets soft set operations restricted gamma operation extended gamma operation |
| title | New restricted and extended soft set operations: restricted gamma and extended gamma operations |
| title_full | New restricted and extended soft set operations: restricted gamma and extended gamma operations |
| title_fullStr | New restricted and extended soft set operations: restricted gamma and extended gamma operations |
| title_full_unstemmed | New restricted and extended soft set operations: restricted gamma and extended gamma operations |
| title_short | New restricted and extended soft set operations: restricted gamma and extended gamma operations |
| title_sort | new restricted and extended soft set operations restricted gamma and extended gamma operations |
| topic | soft sets soft set operations restricted gamma operation extended gamma operation |
| url | https://www.bidacv.com/article_205693_e21f87e355bde6a5826911c6b449a344.pdf |
| work_keys_str_mv | AT aslıhansezgin newrestrictedandextendedsoftsetoperationsrestrictedgammaandextendedgammaoperations AT fitnataybek newrestrictedandextendedsoftsetoperationsrestrictedgammaandextendedgammaoperations |