Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications
We aim through this paper to achieve two goals: first, we define some types of belong and nonbelong relations between ordinary points and double-framed soft sets. These relations are one of the distinguishing characteristics of double-framed soft sets and are somewhat expression of the degrees of me...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9940301 |
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| author | Tareq M. Al-shami Abdelwaheb Mhemdi |
| author_facet | Tareq M. Al-shami Abdelwaheb Mhemdi |
| author_sort | Tareq M. Al-shami |
| collection | DOAJ |
| description | We aim through this paper to achieve two goals: first, we define some types of belong and nonbelong relations between ordinary points and double-framed soft sets. These relations are one of the distinguishing characteristics of double-framed soft sets and are somewhat expression of the degrees of membership and nonmembership. We explore their main properties and determine the conditions under which some of them are equivalent. Also, we introduce the concept of soft mappings between two classes of double-framed soft sets and investigate the relationship between an ordinary point and its image and preimage with respect to the different types of belong and nonbelong relations. By the notions presented herein, many concepts can be studied on double-framed soft topology such as soft separation axioms and cover properties. Second, we give an educational application of optimal choices using the idea of double-framed soft sets. We provide an algorithm of this application with an example to show how this algorithm is carried out. |
| format | Article |
| id | doaj-art-d3aacd1d53754183b3c0ce753f57e915 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d3aacd1d53754183b3c0ce753f57e9152025-02-03T01:28:27ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99403019940301Belong and Nonbelong Relations on Double-Framed Soft Sets and Their ApplicationsTareq M. Al-shami0Abdelwaheb Mhemdi1Department of Mathematics, Sana’a University, Sana’a, YemenDepartment of Mathematics, College of Sciences and Humanities in Aflaj Prince Sattam Bin Abdulaziz University, Riyadh, Saudi ArabiaWe aim through this paper to achieve two goals: first, we define some types of belong and nonbelong relations between ordinary points and double-framed soft sets. These relations are one of the distinguishing characteristics of double-framed soft sets and are somewhat expression of the degrees of membership and nonmembership. We explore their main properties and determine the conditions under which some of them are equivalent. Also, we introduce the concept of soft mappings between two classes of double-framed soft sets and investigate the relationship between an ordinary point and its image and preimage with respect to the different types of belong and nonbelong relations. By the notions presented herein, many concepts can be studied on double-framed soft topology such as soft separation axioms and cover properties. Second, we give an educational application of optimal choices using the idea of double-framed soft sets. We provide an algorithm of this application with an example to show how this algorithm is carried out.http://dx.doi.org/10.1155/2021/9940301 |
| spellingShingle | Tareq M. Al-shami Abdelwaheb Mhemdi Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications Journal of Mathematics |
| title | Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications |
| title_full | Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications |
| title_fullStr | Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications |
| title_full_unstemmed | Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications |
| title_short | Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications |
| title_sort | belong and nonbelong relations on double framed soft sets and their applications |
| url | http://dx.doi.org/10.1155/2021/9940301 |
| work_keys_str_mv | AT tareqmalshami belongandnonbelongrelationsondoubleframedsoftsetsandtheirapplications AT abdelwahebmhemdi belongandnonbelongrelationsondoubleframedsoftsetsandtheirapplications |