Modified Correlation Coefficients for Dual Hesitant Fuzzy Sets Based on the Mean-Range Proximity and Their Applications

Modified Correlation Coefficients for Dual Hesitant Fuzzy Sets Based on the Mean-Range Proximity and Their Applications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Modified Correlation Coefficients for Dual Hesitant Fuzzy Sets Based on the Mean-Range Proximity and Their Applications Shuang Liu, Wangyong Lv, Qian Song, Chaozheng Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9274141/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In the context of dual hesitant fuzzy sets (DHFSs), scholars have proposed multiple definitions of correlation coefficients to capture the correlation between them. However, some existing correlation coefficients still have certain limitations: for example, when DHFSs exhibit a multiplicative relationship or a fixed difference, the correlation coefficient value remains constantly 1; when the number of elements in a DHFS is 2, the correlation coefficient value is always ±1. Under these circumstances, the correlation coefficients fail to describe the differences between different DHFSs, leading to the inability to make correct decisions. To overcome these limitations, we propose a mean-range proximity (MRP) for DHFSs based on the mean difference coefficient and the range difference coefficient. The MRP quantifies the numerical differences between DHFSs. Subsequently, we put forward the modified correlation coefficients by incorporating the MRP, rigorously prove their properties, and demonstrate that they resolve the identified limitations. Finally, we apply the modified correlation coefficients to multi-attribute decision-making problems in three distinct scenarios, validating the effectiveness and rationality of the proposed method in practical contexts. Dual hesitant fuzzy sets Mean-range proximity Modified correlation coefficient Multi-attribute decision-making problems Unmanned aerial vehicle Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9274141","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":619610669,"identity":"cfefeb3f-0fde-4340-a6ff-ee3d6c07ce95","order_by":0,"name":"Shuang Liu","email":"","orcid":"","institution":"Sichuan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Shuang","middleName":"","lastName":"Liu","suffix":""},{"id":619610670,"identity":"55378a7e-5cd1-488c-b87e-b95d593e3818","order_by":1,"name":"Wangyong Lv","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8ElEQVRIiWNgGAWjYBACPgST+QBDAoRlgFcLGxIzgWQtPHCVBLRI5Bh+Lvh1WM6cf83nDw9q7iQ2sDdvk2CouYNPi7H0zL7DxpYz3m6TSDj2LLGB51iZBMOxZ7i18JzdIM3bczhxw42z2xgSGw4nNkjkmEkwNhzGp2Xzb4iWM48/gLXIvyGghb13mzTPD6CW8z0MEhBbeAhp6f9mzduQbmxwg80M6JfDxm08acUWQAZOLfzMbMm3ef5YyxmcP/z444+aw7L97Ic33vhQg1sLGDC2NTMwSCRA7QURCfg1AMGfOqB9BwgqGwWjYBSMghEKAMP6WU12hF6MAAAAAElFTkSuQmCC","orcid":"","institution":"Sichuan Normal University","correspondingAuthor":true,"prefix":"","firstName":"Wangyong","middleName":"","lastName":"Lv","suffix":""},{"id":619610671,"identity":"886bc290-50b0-4267-803d-ad20b2a9928b","order_by":2,"name":"Qian Song","email":"","orcid":"","institution":"Sichuan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Qian","middleName":"","lastName":"Song","suffix":""},{"id":619610672,"identity":"37d93d9d-826b-460d-998c-3533ce8da136","order_by":3,"name":"Chaozheng Zhang","email":"","orcid":"","institution":"Sichuan Normal University","correspondingAuthor":false,"prefix":"","firstName":"Chaozheng","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-03-31 04:08:56","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9274141/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9274141/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108715256,"identity":"5eaa3d32-6afc-459d-a99d-ad6145aeb8ad","added_by":"auto","created_at":"2026-05-07 14:57:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":524359,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9274141/v1_covered_a99fcda1-8fb4-4fad-a505-de5978a39852.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modified Correlation Coefficients for Dual Hesitant Fuzzy Sets Based on the Mean-Range Proximity and Their Applications","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Dual hesitant fuzzy sets, Mean-range proximity, Modified correlation coefficient, Multi-attribute decision-making problems, Unmanned aerial vehicle","lastPublishedDoi":"10.21203/rs.3.rs-9274141/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9274141/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In the context of dual hesitant fuzzy sets (DHFSs), scholars have proposed multiple definitions of correlation coefficients to capture the correlation between them. 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