An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning
The concept of Fermatean fuzzy set offers a more comprehensive perspective on Pythagorean fuzzy sets, with greater potential for practical applications due to its broader scope compared to Pythagorean fuzzy sets. In contrast, distance measures serve as effective information measures in decision-maki...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10378699/ |
| _version_ | 1797357089858781184 |
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| author | Abdul Haseeb Ganie Nadia El Mokhtar Gheith Yousef Al-Qudah Abdul Hamid Ganie Sunny Kumar Sharma Amal M. Aqlan Mohammed M. Khalaf |
| author_facet | Abdul Haseeb Ganie Nadia El Mokhtar Gheith Yousef Al-Qudah Abdul Hamid Ganie Sunny Kumar Sharma Amal M. Aqlan Mohammed M. Khalaf |
| author_sort | Abdul Haseeb Ganie |
| collection | DOAJ |
| description | The concept of Fermatean fuzzy set offers a more comprehensive perspective on Pythagorean fuzzy sets, with greater potential for practical applications due to its broader scope compared to Pythagorean fuzzy sets. In contrast, distance measures serve as effective information measures in decision-making using deep learning methods. This research paper introduces a novel distance measure within the Fermatean fuzzy framework. This new distance measure exhibit enhanced performance indices compared to existing distance measures discussed in previous literature. The newly proposed distance operators based on Fermatean fuzzy sets offer a fresh approach by considering all three membership functions of Fermatean fuzzy sets, which differs from existing practices. This distance operator also incorporate all membership functions to prevent errors caused by exclusions, which have been observed in other distance operators. Several theorems are provided to validate the alignment of this new Fermatean fuzzy distance technique with properties expected of distance operators. The comparative analysis of the newly introduced Fermatean fuzzy distance measure with similar existing distance techniques is conducted through numerical comparison and also in relation to their applications, aiming to highlight the superiority of the proposed Pythagorean fuzzy distance techniques over the existing ones. The application of the proposed Fermatean fuzzy distance measure is demonstrated in scenarios involving pattern classification and bidirectional approximate reasoning. |
| first_indexed | 2024-03-08T14:38:24Z |
| format | Article |
| id | doaj.art-759295fff3d54295af559c493ce11580 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-08T14:38:24Z |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-759295fff3d54295af559c493ce115802024-01-12T00:02:28ZengIEEEIEEE Access2169-35362024-01-01124780479110.1109/ACCESS.2023.334878010378699An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate ReasoningAbdul Haseeb Ganie0https://orcid.org/0000-0002-0136-7758Nadia El Mokhtar Gheith1Yousef Al-Qudah2https://orcid.org/0000-0001-5952-4990Abdul Hamid Ganie3https://orcid.org/0000-0002-1787-5036Sunny Kumar Sharma4https://orcid.org/0009-0009-6760-315XAmal M. Aqlan5Mohammed M. Khalaf6Department of Mathematics, National Institute of Technology Warangal, Warangal, IndiaDepartment of Mathematical Sciences, School of Basic Sciences, Libyan Academy for Postgraduate Studies, Janzur, LibyaDepartment of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman, JordanDepartment of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh, Saudi ArabiaDepartment of Mathematics, Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education, Manipal, Karnataka, IndiaDepartment of Computer Sciences, Applied College, King Khalid University, Muhayil, Saudi ArabiaDepartment of Mathematics, Higher Institute of Engineering and Technology, King Mariout, EgyptThe concept of Fermatean fuzzy set offers a more comprehensive perspective on Pythagorean fuzzy sets, with greater potential for practical applications due to its broader scope compared to Pythagorean fuzzy sets. In contrast, distance measures serve as effective information measures in decision-making using deep learning methods. This research paper introduces a novel distance measure within the Fermatean fuzzy framework. This new distance measure exhibit enhanced performance indices compared to existing distance measures discussed in previous literature. The newly proposed distance operators based on Fermatean fuzzy sets offer a fresh approach by considering all three membership functions of Fermatean fuzzy sets, which differs from existing practices. This distance operator also incorporate all membership functions to prevent errors caused by exclusions, which have been observed in other distance operators. Several theorems are provided to validate the alignment of this new Fermatean fuzzy distance technique with properties expected of distance operators. The comparative analysis of the newly introduced Fermatean fuzzy distance measure with similar existing distance techniques is conducted through numerical comparison and also in relation to their applications, aiming to highlight the superiority of the proposed Pythagorean fuzzy distance techniques over the existing ones. The application of the proposed Fermatean fuzzy distance measure is demonstrated in scenarios involving pattern classification and bidirectional approximate reasoning.https://ieeexplore.ieee.org/document/10378699/Bidirectional approximate reasoningdistance measurefuzzy setfermatean fuzzy setpattern analysissimilarity measure |
| spellingShingle | Abdul Haseeb Ganie Nadia El Mokhtar Gheith Yousef Al-Qudah Abdul Hamid Ganie Sunny Kumar Sharma Amal M. Aqlan Mohammed M. Khalaf An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning IEEE Access Bidirectional approximate reasoning distance measure fuzzy set fermatean fuzzy set pattern analysis similarity measure |
| title | An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning |
| title_full | An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning |
| title_fullStr | An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning |
| title_full_unstemmed | An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning |
| title_short | An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning |
| title_sort | innovative fermatean fuzzy distance metric with its application in classification and bidirectional approximate reasoning |
| topic | Bidirectional approximate reasoning distance measure fuzzy set fermatean fuzzy set pattern analysis similarity measure |
| url | https://ieeexplore.ieee.org/document/10378699/ |
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