Topological Approaches for Rough Continuous Functions with Applications
In this paper, we purposed further study on rough functions and introduced some concepts based on it. We introduced and investigated the concepts of topological lower and upper approximations of near-open sets and studied their basic properties. We defined and studied new topological neighborhood ap...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5586187 |
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| _version_ | 1832566433995816960 |
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| author | A. S. Salama A. Mhemdi O. G. Elbarbary T. M. Al-shami |
| author_facet | A. S. Salama A. Mhemdi O. G. Elbarbary T. M. Al-shami |
| author_sort | A. S. Salama |
| collection | DOAJ |
| description | In this paper, we purposed further study on rough functions and introduced some concepts based on it. We introduced and investigated the concepts of topological lower and upper approximations of near-open sets and studied their basic properties. We defined and studied new topological neighborhood approach of rough functions. We generalized rough functions to topological rough continuous functions by different topological structures. In addition, topological approximations of a function as a relation were defined and studied. Finally, we applied our approach of rough functions in finding the images of patient classification data using rough continuous functions. |
| format | Article |
| id | doaj-art-b856b4f4f5ce4fc481d80f92fc7053c5 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b856b4f4f5ce4fc481d80f92fc7053c52025-02-03T01:04:14ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/55861875586187Topological Approaches for Rough Continuous Functions with ApplicationsA. S. Salama0A. Mhemdi1O. G. Elbarbary2T. M. Al-shami3Department of Mathematics, Faculty of Science, Tanta University, Tanta, EgyptDepartment of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam Bin Abdulaziz University, Riyadh, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Tanta University, Tanta, EgyptDepartment of Mathematics, Sanaʼa University, Sanaʼa, YemenIn this paper, we purposed further study on rough functions and introduced some concepts based on it. We introduced and investigated the concepts of topological lower and upper approximations of near-open sets and studied their basic properties. We defined and studied new topological neighborhood approach of rough functions. We generalized rough functions to topological rough continuous functions by different topological structures. In addition, topological approximations of a function as a relation were defined and studied. Finally, we applied our approach of rough functions in finding the images of patient classification data using rough continuous functions.http://dx.doi.org/10.1155/2021/5586187 |
| spellingShingle | A. S. Salama A. Mhemdi O. G. Elbarbary T. M. Al-shami Topological Approaches for Rough Continuous Functions with Applications Complexity |
| title | Topological Approaches for Rough Continuous Functions with Applications |
| title_full | Topological Approaches for Rough Continuous Functions with Applications |
| title_fullStr | Topological Approaches for Rough Continuous Functions with Applications |
| title_full_unstemmed | Topological Approaches for Rough Continuous Functions with Applications |
| title_short | Topological Approaches for Rough Continuous Functions with Applications |
| title_sort | topological approaches for rough continuous functions with applications |
| url | http://dx.doi.org/10.1155/2021/5586187 |
| work_keys_str_mv | AT assalama topologicalapproachesforroughcontinuousfunctionswithapplications AT amhemdi topologicalapproachesforroughcontinuousfunctionswithapplications AT ogelbarbary topologicalapproachesforroughcontinuousfunctionswithapplications AT tmalshami topologicalapproachesforroughcontinuousfunctionswithapplications |