Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets
This paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal l defined on a fuzzy approximation space X,R. This definition considered the degree r∈0,1 in defining the after sets and the before sets of the arbitrary fuzzy relation R on the finite set of objects X. It is shown tha...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/1489444 |
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| _version_ | 1832569142365913088 |
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| author | S. H. Alsulami S. E. Abbas S. Saleh Ismail Ibedou |
| author_facet | S. H. Alsulami S. E. Abbas S. Saleh Ismail Ibedou |
| author_sort | S. H. Alsulami |
| collection | DOAJ |
| description | This paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal l defined on a fuzzy approximation space X,R. This definition considered the degree r∈0,1 in defining the after sets and the before sets of the arbitrary fuzzy relation R on the finite set of objects X. It is shown that this new type of roughness is a generalization to many of previous definitions in the fuzzy case and also in the ordinary case. As an application, it is given a rough fuzzy-connected set notion depending on some degree r∈0,1. |
| format | Article |
| id | doaj-art-a5464364bca74d59aa6d2d4c807d91ac |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a5464364bca74d59aa6d2d4c807d91ac2025-02-02T23:07:38ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/1489444Using the Degree r∈[0,1] in Defining Rough Fuzzy SetsS. H. Alsulami0S. E. Abbas1S. Saleh2Ismail Ibedou3Department of Mathematics and StatisticsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsThis paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal l defined on a fuzzy approximation space X,R. This definition considered the degree r∈0,1 in defining the after sets and the before sets of the arbitrary fuzzy relation R on the finite set of objects X. It is shown that this new type of roughness is a generalization to many of previous definitions in the fuzzy case and also in the ordinary case. As an application, it is given a rough fuzzy-connected set notion depending on some degree r∈0,1.http://dx.doi.org/10.1155/2024/1489444 |
| spellingShingle | S. H. Alsulami S. E. Abbas S. Saleh Ismail Ibedou Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets Journal of Mathematics |
| title | Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets |
| title_full | Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets |
| title_fullStr | Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets |
| title_full_unstemmed | Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets |
| title_short | Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets |
| title_sort | using the degree r∈ 0 1 in defining rough fuzzy sets |
| url | http://dx.doi.org/10.1155/2024/1489444 |
| work_keys_str_mv | AT shalsulami usingthedegreer01indefiningroughfuzzysets AT seabbas usingthedegreer01indefiningroughfuzzysets AT ssaleh usingthedegreer01indefiningroughfuzzysets AT ismailibedou usingthedegreer01indefiningroughfuzzysets |