Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects
The fuzzy set generally identifies the topological relationship between two vague spatial objects. Indeterminacy can arise at any point in the modelling process, and the fuzzy model is unable to deal with this. Given that the Pythagorean fuzzy is better equipped to deal with indeterminacies than the...
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| Format: | Article |
| Language: | English |
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Ayandegan Institute of Higher Education,
2024-06-01
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| Series: | Journal of Fuzzy Extension and Applications |
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| Online Access: | https://www.journal-fea.com/article_192201_9e87d8b60555b68508f19f9a9083cdbb.pdf |
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| author | Subhankar Jana Anjali Patel Juthika Mahanta |
| author_facet | Subhankar Jana Anjali Patel Juthika Mahanta |
| author_sort | Subhankar Jana |
| collection | DOAJ |
| description | The fuzzy set generally identifies the topological relationship between two vague spatial objects. Indeterminacy can arise at any point in the modelling process, and the fuzzy model is unable to deal with this. Given that the Pythagorean fuzzy is better equipped to deal with indeterminacies than the fuzzy set, we advocated using Pythagorean fuzzy modelling to determine the topological relation between two spatial objects. This paper contributes to the expanding study of Pythagorean fuzzy topological spaces by introducing core, fringe, outer, regular open set, regular closed set, double connectedness and homeomorphism in Pythagorean fuzzy environment. Using these definitions, the paper proposes an algebraic model, namely the pythagorean fuzzy 9-intersection matrix, to find topological relations between any two Pythagorean fuzzy sets in a Pythagorean topological space. The inbuilt capability of the PFS to handle indeterminacy establishes the proposed model as the potential tool to find topological relations between two indeterminate spatial objects. Ample instances are discussed to nourish the existence of indeterminate spatial objects. Finally, a simple Pythagorean fuzzy region is defined and all possible relations between such two Pythagorean fuzzy regions are examined. |
| format | Article |
| id | doaj-art-75245a3e7e4f49818e938d801633a1b7 |
| institution | Kabale University |
| issn | 2783-1442 2717-3453 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Ayandegan Institute of Higher Education, |
| record_format | Article |
| series | Journal of Fuzzy Extension and Applications |
| spelling | doaj-art-75245a3e7e4f49818e938d801633a1b72025-01-30T15:07:06ZengAyandegan Institute of Higher Education,Journal of Fuzzy Extension and Applications2783-14422717-34532024-06-015225127410.22105/jfea.2024.426562.1342192201Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objectsSubhankar Jana0Anjali Patel1Juthika Mahanta2Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, 788010, India.Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, 788010, India.Department of Mathematics, National Institute of Technology Silchar, Silchar, Assam, 788010, India.The fuzzy set generally identifies the topological relationship between two vague spatial objects. Indeterminacy can arise at any point in the modelling process, and the fuzzy model is unable to deal with this. Given that the Pythagorean fuzzy is better equipped to deal with indeterminacies than the fuzzy set, we advocated using Pythagorean fuzzy modelling to determine the topological relation between two spatial objects. This paper contributes to the expanding study of Pythagorean fuzzy topological spaces by introducing core, fringe, outer, regular open set, regular closed set, double connectedness and homeomorphism in Pythagorean fuzzy environment. Using these definitions, the paper proposes an algebraic model, namely the pythagorean fuzzy 9-intersection matrix, to find topological relations between any two Pythagorean fuzzy sets in a Pythagorean topological space. The inbuilt capability of the PFS to handle indeterminacy establishes the proposed model as the potential tool to find topological relations between two indeterminate spatial objects. Ample instances are discussed to nourish the existence of indeterminate spatial objects. Finally, a simple Pythagorean fuzzy region is defined and all possible relations between such two Pythagorean fuzzy regions are examined.https://www.journal-fea.com/article_192201_9e87d8b60555b68508f19f9a9083cdbb.pdfpythagorean fuzzy setpythagorean fuzzy topology9-intersection matrixgisvague object modelling |
| spellingShingle | Subhankar Jana Anjali Patel Juthika Mahanta Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects Journal of Fuzzy Extension and Applications pythagorean fuzzy set pythagorean fuzzy topology 9-intersection matrix gis vague object modelling |
| title | Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects |
| title_full | Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects |
| title_fullStr | Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects |
| title_full_unstemmed | Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects |
| title_short | Decomposition of a Pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects |
| title_sort | decomposition of a pythagorean fuzzy topological space and its application in determining topological relations between indeterminate spatial objects |
| topic | pythagorean fuzzy set pythagorean fuzzy topology 9-intersection matrix gis vague object modelling |
| url | https://www.journal-fea.com/article_192201_9e87d8b60555b68508f19f9a9083cdbb.pdf |
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