Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis
The picture hesitant fuzzy set (PHFS) integrates elements of picture fuzzy sets and hesitant fuzzy sets, incorporating membership, abstinence, and non-membership degrees to provide a robust framework for addressing uncertainties and complex data in real-world scenarios. In this study, we introduce k...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025013 |
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| author | Noura Omair Alshehri Rania Saeed Alghamdi Noura Awad Al Qarni |
| author_facet | Noura Omair Alshehri Rania Saeed Alghamdi Noura Awad Al Qarni |
| author_sort | Noura Omair Alshehri |
| collection | DOAJ |
| description | The picture hesitant fuzzy set (PHFS) integrates elements of picture fuzzy sets and hesitant fuzzy sets, incorporating membership, abstinence, and non-membership degrees to provide a robust framework for addressing uncertainties and complex data in real-world scenarios. In this study, we introduce key characteristics of picture hesitant fuzzy elements, including average functions, variance functions, and hesitancy degrees, to enhance its descriptive capability. Based on these characteristics, we proposed novel distance measures for PHFS. Further, we investigated their properties and proved the triangle inequality of distance measure. These measures were systematically applied in a medical diagnostic context, where they demonstrated significant improvements in diagnostic accuracy by effectively distinguishing patient conditions. Sensitivity analyses and comparative evaluations further validated the practicality and robustness of the proposed methods, highlighting their potential for broader applications in decision-making under uncertainty. |
| format | Article |
| id | doaj-art-e9f7648e63d94e3ba5545ad12a019477 |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e9f7648e63d94e3ba5545ad12a0194772025-08-20T02:43:12ZengAIMS PressAIMS Mathematics2473-69882025-01-0110127028810.3934/math.2025013Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosisNoura Omair Alshehri0Rania Saeed Alghamdi1Noura Awad Al Qarni2Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaThe picture hesitant fuzzy set (PHFS) integrates elements of picture fuzzy sets and hesitant fuzzy sets, incorporating membership, abstinence, and non-membership degrees to provide a robust framework for addressing uncertainties and complex data in real-world scenarios. In this study, we introduce key characteristics of picture hesitant fuzzy elements, including average functions, variance functions, and hesitancy degrees, to enhance its descriptive capability. Based on these characteristics, we proposed novel distance measures for PHFS. Further, we investigated their properties and proved the triangle inequality of distance measure. These measures were systematically applied in a medical diagnostic context, where they demonstrated significant improvements in diagnostic accuracy by effectively distinguishing patient conditions. Sensitivity analyses and comparative evaluations further validated the practicality and robustness of the proposed methods, highlighting their potential for broader applications in decision-making under uncertainty.https://www.aimspress.com/article/doi/10.3934/math.2025013picture hesitant fuzzy setcharacteristicdistance measurehesitancy degreemedical diagnosis |
| spellingShingle | Noura Omair Alshehri Rania Saeed Alghamdi Noura Awad Al Qarni Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis AIMS Mathematics picture hesitant fuzzy set characteristic distance measure hesitancy degree medical diagnosis |
| title | Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis |
| title_full | Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis |
| title_fullStr | Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis |
| title_full_unstemmed | Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis |
| title_short | Development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis |
| title_sort | development of novel distance measures for picture hesitant fuzzy sets and their application in medical diagnosis |
| topic | picture hesitant fuzzy set characteristic distance measure hesitancy degree medical diagnosis |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025013 |
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