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...

Full description

Saved in:
Bibliographic Details
Main Authors: Noura Omair Alshehri, Rania Saeed Alghamdi, Noura Awad Al Qarni
Format: Article
Language:English
Published: AIMS Press 2025-01-01
Series:AIMS Mathematics
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2025013
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850087523547611136
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
work_keys_str_mv AT nouraomairalshehri developmentofnoveldistancemeasuresforpicturehesitantfuzzysetsandtheirapplicationinmedicaldiagnosis
AT raniasaeedalghamdi developmentofnoveldistancemeasuresforpicturehesitantfuzzysetsandtheirapplicationinmedicaldiagnosis
AT nouraawadalqarni developmentofnoveldistancemeasuresforpicturehesitantfuzzysetsandtheirapplicationinmedicaldiagnosis