Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making
Abstract As an advanced extension of intuitionistic fuzzy sets (IFSs), Fermatean fuzzy sets (FFSs) serve as powerful methods for managing uncertainties in complicated problem-solving contexts. When working with Fermatean fuzzy information, distance measures are fundamental in measuring the differenc...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Springer
2025-05-01
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| Series: | Discover Applied Sciences |
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| Online Access: | https://doi.org/10.1007/s42452-025-07042-w |
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| author | Yuhan Li Sijia Zhu Juan Liao Xue Han Zhe Liu |
| author_facet | Yuhan Li Sijia Zhu Juan Liao Xue Han Zhe Liu |
| author_sort | Yuhan Li |
| collection | DOAJ |
| description | Abstract As an advanced extension of intuitionistic fuzzy sets (IFSs), Fermatean fuzzy sets (FFSs) serve as powerful methods for managing uncertainties in complicated problem-solving contexts. When working with Fermatean fuzzy information, distance measures are fundamental in measuring the differences between two FFSs. These measures are essential to accurately assess and compare the variations in fuzzy data. However, accurately measuring the distance between two FFSs is still challenging and requires further exploration. We propose two novel distance measures for FFSs. Moreover, we demonstrate that the proposed distance measures meet the necessary axiomatic conditions. Afterwards, we present numerical examples to highlight the superiority of the proposed measures compared to those already available. Finally, we apply the proposed distance measures to pattern classification and multi-attribute decision-making (MADM) problems. Experimental results show that the proposed measures improve classification performance and decision-making efficiency. Specifically, they enhance pattern recognition in autonomous driving systems and improve strategic investment decision-making in sustainable transportation. |
| format | Article |
| id | doaj-art-26e2837da975413c88df078705d3011d |
| institution | Kabale University |
| issn | 3004-9261 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Springer |
| record_format | Article |
| series | Discover Applied Sciences |
| spelling | doaj-art-26e2837da975413c88df078705d3011d2025-08-20T03:48:18ZengSpringerDiscover Applied Sciences3004-92612025-05-017612010.1007/s42452-025-07042-wEstablishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-makingYuhan Li0Sijia Zhu1Juan Liao2Xue Han3Zhe Liu4Cw Chu College, Jiangsu Normal UniversityCw Chu College, Jiangsu Normal UniversitySchool of Computer Sciences, Universiti Sains MalaysiaSchool of Management, Xi’an University of Architecture and TechnologySchool of Computer Sciences, Universiti Sains MalaysiaAbstract As an advanced extension of intuitionistic fuzzy sets (IFSs), Fermatean fuzzy sets (FFSs) serve as powerful methods for managing uncertainties in complicated problem-solving contexts. When working with Fermatean fuzzy information, distance measures are fundamental in measuring the differences between two FFSs. These measures are essential to accurately assess and compare the variations in fuzzy data. However, accurately measuring the distance between two FFSs is still challenging and requires further exploration. We propose two novel distance measures for FFSs. Moreover, we demonstrate that the proposed distance measures meet the necessary axiomatic conditions. Afterwards, we present numerical examples to highlight the superiority of the proposed measures compared to those already available. Finally, we apply the proposed distance measures to pattern classification and multi-attribute decision-making (MADM) problems. Experimental results show that the proposed measures improve classification performance and decision-making efficiency. Specifically, they enhance pattern recognition in autonomous driving systems and improve strategic investment decision-making in sustainable transportation.https://doi.org/10.1007/s42452-025-07042-wFermatean fuzzy setsDistance measurePattern classificationMulti-attribute decision-making |
| spellingShingle | Yuhan Li Sijia Zhu Juan Liao Xue Han Zhe Liu Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making Discover Applied Sciences Fermatean fuzzy sets Distance measure Pattern classification Multi-attribute decision-making |
| title | Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making |
| title_full | Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making |
| title_fullStr | Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making |
| title_full_unstemmed | Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making |
| title_short | Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making |
| title_sort | establishment of distance measures on fermatean fuzzy sets and their applications in pattern classification and multi attribute decision making |
| topic | Fermatean fuzzy sets Distance measure Pattern classification Multi-attribute decision-making |
| url | https://doi.org/10.1007/s42452-025-07042-w |
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