A PROBID Hybrid Decision Model Based on Multi-Valued Neutrosophic Sets and Contact Numbers Integration

A PROBID Hybrid Decision Model Based on Multi-Valued Neutrosophic Sets and Contact Numbers Integration | 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 A PROBID Hybrid Decision Model Based on Multi-Valued Neutrosophic Sets and Contact Numbers Integration Dongsheng Xu, Cedong Wang, Lijuan Hu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8318774/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 Multiple attribute decision making (MADM) is a vital part of modern decision science and often faces challenges in representing fuzzy information and maintaining dynamic adaptability under complex uncertain conditions. Although existing studies seek to improve heterogeneous information fusion using fuzzy set theory, research gaps persist in dynamic fuzzy decision mechanisms, reduction of subjective factors, and validation in multi-dimensional scenarios. The classic PROBID method, leveraging an ideal-average distance mechanism, has demonstrated considerable effectiveness across various domains. Yet, its strong sensitivity to attribute weight changes and limited adaptability in static contexts restrict broader applicability. To overcome these issues, this research proposes a hybrid model named multivalued neutrosophic contact numbers-based PROBID (MVCN-PROBID). By integrating the ternary semantic representation of multi-valued neutrosophic numbers (MVNNs) with the identity, discrepancy, and contrary theoretical mechanisms of contact numbers (CNs) in set pair analysis (SPA), a dual-dimensional dynamic evaluation system is established. This synergy within the PROBID framework partially alleviates traditional decision-making bottlenecks in dynamic fuzzy environments. Empirical analysis using two cases, agricultural drone procurement and investment firm selection, shows that MVCN-PROBID produces priority rankings closely matching practical needs. Internal robustness was examined via systematic parameter adjustments, and consistency was verified through multi-method comparative ranking, confirming the model's advantages in stability, applicability, and reliability. This work extends the PROBID method’s theoretical boundaries under a fuzzy mathematics framework, offering a structured solution for MADM in complex settings. Multiple attribute decision making Multi-valued Neutrosophic Sets Set Pair Analysis Contact Numbers PROBID method Full Text Additional Declarations No competing interests reported. Supplementary Files Summaryofthetablesinthemanuscript.docx attributeweightadjustmentsituations.xlsx 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8318774","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":567087982,"identity":"8cbcca95-b0ef-406b-beb7-ec4397b448fd","order_by":0,"name":"Dongsheng Xu","email":"","orcid":"","institution":"Southwest Petroleum University","correspondingAuthor":false,"prefix":"","firstName":"Dongsheng","middleName":"","lastName":"Xu","suffix":""},{"id":567087984,"identity":"1235b263-3e17-44d7-8c1d-782452be3c80","order_by":1,"name":"Cedong Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIie3QsWrDMBCAYQmBs6j7mYLzChaCkiGQV5EpeCqlUCgOlFYlYC0KXR0ofYZAIPMZQbuYzi50SQKZ/QINyQME29066Jvvh7sjxPP+pxhVdoioeW0QMoiGPRKBTYWSWRQ4qkZS6O5EloscE1MoidM8Swh2bfXplu4i/6Fziwq/30FRzTbbui2p0jvHv/YsNBrLxRpuBySQ8qYluap57PgDC4QttQvXcE81Dy67k4DxSX1N3O8bJBp7JGWRO6BFSjDUPZLJ6ZbTk9OY2oogfIAUs45bQuNWjcrGzy/GsgYen6LhYLbZtSVnsL+Ne57neWccAee1Wt5fLEDPAAAAAElFTkSuQmCC","orcid":"","institution":"Southwest Petroleum University","correspondingAuthor":true,"prefix":"","firstName":"Cedong","middleName":"","lastName":"Wang","suffix":""},{"id":567087986,"identity":"e03914c7-a693-46c8-a96c-a963eb10aaae","order_by":2,"name":"Lijuan Hu","email":"","orcid":"","institution":"Southwest Petroleum University","correspondingAuthor":false,"prefix":"","firstName":"Lijuan","middleName":"","lastName":"Hu","suffix":""}],"badges":[],"createdAt":"2025-12-09 14:23:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8318774/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8318774/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99284035,"identity":"d3bbe734-dcc2-4c42-845d-2dca41b63643","added_by":"auto","created_at":"2025-12-31 09:07:00","extension":"jpg","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":44487,"visible":true,"origin":"","legend":"","description":"","filename":"1.structureofCNs.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/089bfee9d4889add51f061b1.jpg"},{"id":99284038,"identity":"c64688db-a971-4852-8a61-8207f0c63c35","added_by":"auto","created_at":"2025-12-31 09:07:00","extension":"jpg","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":133422,"visible":true,"origin":"","legend":"","description":"","filename":"2.System.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/2cc684caad184e5ea0232b58.jpg"},{"id":99284040,"identity":"10b25e3c-cebb-4d67-a5d4-3173b7e09561","added_by":"auto","created_at":"2025-12-31 09:07:00","extension":"jpg","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":175850,"visible":true,"origin":"","legend":"","description":"","filename":"3.lorenzcurve.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/7e8385babdaea04c52e91ba9.jpg"},{"id":99320700,"identity":"02f6fefb-6372-448b-b1c9-2f3e9948d7e3","added_by":"auto","created_at":"2025-12-31 16:38:52","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":56667,"visible":true,"origin":"","legend":"","description":"","filename":"Summaryofthetablesinthemanuscript.docx","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/b6af0d627d6479b371962570.docx"},{"id":99284042,"identity":"85a99161-cab6-4e9e-91c2-282a6ffcb765","added_by":"auto","created_at":"2025-12-31 09:07:00","extension":"docx","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":993694,"visible":true,"origin":"","legend":"","description":"","filename":"APROBIDHybridDecisionModel.docx","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/e9bd7d3811c570afdbc13c81.docx"},{"id":99284051,"identity":"f04a9fba-87c9-42e7-ba1b-948055f42eb7","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"jpg","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6957352,"visible":true,"origin":"","legend":"","description":"","filename":"4.sensitivityanalysiradar.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/a30d9349ed4deefe9572a120.jpg"},{"id":99284046,"identity":"d37be3e4-4f8e-4ce4-ad51-47c29764a917","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"jpg","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":147575,"visible":true,"origin":"","legend":"","description":"","filename":"5.110weightschemes.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/74910ef216d260298e68e140.jpg"},{"id":99318947,"identity":"34d780eb-c337-4fd5-9295-845e25d862d4","added_by":"auto","created_at":"2025-12-31 16:35:46","extension":"jpg","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":325964,"visible":true,"origin":"","legend":"","description":"","filename":"6.Theradarchartof110.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/ee1b968da3b5b031633c1d3b.jpg"},{"id":99319500,"identity":"cd7c8320-03f7-47bc-897d-01a99c7bc283","added_by":"auto","created_at":"2025-12-31 16:37:24","extension":"jpg","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":246865,"visible":true,"origin":"","legend":"","description":"","filename":"7.Spearmanheatmap.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/f7ec5e19e7d3fef8ce1bb597.jpg"},{"id":99284041,"identity":"97d5c71c-b5fa-4282-b16c-a03fa275d184","added_by":"auto","created_at":"2025-12-31 09:07:00","extension":"json","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5382,"visible":true,"origin":"","legend":"","description":"","filename":"3ce4bd3afe72472fa08deb80f607ecfe.json","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/36a67213f3370633dc14882a.json"},{"id":99319428,"identity":"cf9d8079-0952-4d7c-af4f-6923595cdfc5","added_by":"auto","created_at":"2025-12-31 16:37:12","extension":"xlsx","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":15359,"visible":true,"origin":"","legend":"","description":"","filename":"attributeweightadjustmentsituations.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/813fe28592863c2d8f010da1.xlsx"},{"id":99319489,"identity":"1cd8175a-254d-4ada-957f-101659dad608","added_by":"auto","created_at":"2025-12-31 16:37:22","extension":"xml","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":395952,"visible":true,"origin":"","legend":"","description":"","filename":"3ce4bd3afe72472fa08deb80f607ecfe1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/1bf90f70464245f22afc12b0.xml"},{"id":99318908,"identity":"9a074bfc-571e-4228-a144-c341acaa4d99","added_by":"auto","created_at":"2025-12-31 16:35:44","extension":"jpg","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":44487,"visible":true,"origin":"","legend":"","description":"","filename":"1.structureofCNs.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/b7f0c57e88a094af846551c6.jpg"},{"id":99319529,"identity":"7f1efc81-f4d2-4a19-8dcb-ff9036cfd6ba","added_by":"auto","created_at":"2025-12-31 16:37:26","extension":"jpg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":133422,"visible":true,"origin":"","legend":"","description":"","filename":"2.System.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/4ca8aab038fdb297fc23c7f5.jpg"},{"id":99284054,"identity":"c4f616b8-a320-42be-8bc7-ab327992a70e","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"jpg","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":175850,"visible":true,"origin":"","legend":"","description":"","filename":"3.lorenzcurve.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/be2d48ad19efc481257aac60.jpg"},{"id":99284068,"identity":"bf9c8c3c-b276-4132-91cf-10e179b33d89","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"jpg","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6957352,"visible":true,"origin":"","legend":"","description":"","filename":"4.sensitivityanalysiradar.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/9c6e4498329d4f9f1aafb84f.jpg"},{"id":99320796,"identity":"47eb85f6-bf1e-454b-bdf9-7e2da7a8f584","added_by":"auto","created_at":"2025-12-31 16:38:54","extension":"jpg","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":147575,"visible":true,"origin":"","legend":"","description":"","filename":"5.110weightschemes.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/2c388285628aca94879f2b7b.jpg"},{"id":99284057,"identity":"d617f2dc-301e-46e6-9dcf-b1b44606c0c3","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"jpg","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":325964,"visible":true,"origin":"","legend":"","description":"","filename":"6.Theradarchartof110.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/94db16c3063e4272ceec6438.jpg"},{"id":99320755,"identity":"804b5ca7-a281-4db7-a3eb-f5f2d430ecff","added_by":"auto","created_at":"2025-12-31 16:38:53","extension":"jpg","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":246865,"visible":true,"origin":"","legend":"","description":"","filename":"7.Spearmanheatmap.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/14c29cdcae3ce5a3487908b7.jpg"},{"id":99321358,"identity":"71e41ec2-5cdd-4f70-9b21-bc2576d5ba6b","added_by":"auto","created_at":"2025-12-31 16:39:20","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":37260,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/f1b971bf1f74ee83afc6383c.png"},{"id":99284059,"identity":"7b070e38-210c-4f73-9aca-eb79c64d116e","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":111830,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/3a3f68b3e397f45b317f037b.png"},{"id":99320439,"identity":"9d0e9866-e415-4441-b34a-ce2e30d1aea3","added_by":"auto","created_at":"2025-12-31 16:38:35","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":133674,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/696670517fbafc3345139512.png"},{"id":99320163,"identity":"d781e26b-d1f1-41f5-93a6-e338aaad1030","added_by":"auto","created_at":"2025-12-31 16:38:20","extension":"jpeg","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":98876,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/8a2279a029df81219e88b646.jpeg"},{"id":99321375,"identity":"fd10836e-37e7-4155-bca1-36adf55de6df","added_by":"auto","created_at":"2025-12-31 16:39:21","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":161499,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/e0e510bb87a5212c96418dce.png"},{"id":99284063,"identity":"1b48c594-52aa-4022-abd4-fa4b2ab8de5a","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":296512,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/f7bba0ac85e3583b65731696.png"},{"id":99321366,"identity":"4d52cac3-4bef-495b-aec0-a6b159f3c4d3","added_by":"auto","created_at":"2025-12-31 16:39:21","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":49612,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/d7d2cf17c5465b8af9ff48c1.png"},{"id":99284065,"identity":"c2406054-edd8-4dcc-9427-1ac592bd537e","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":12799,"visible":true,"origin":"","legend":"","description":"","filename":"Online1.structureofCNs.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/5d487569f3dab97a2a73dbe0.png"},{"id":99284069,"identity":"45255e68-8c0b-418d-ae4f-5cd10e0d797e","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":49123,"visible":true,"origin":"","legend":"","description":"","filename":"Online2.System.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/da212090fd96ce54cfb7ab2b.png"},{"id":99284061,"identity":"4f865f8d-aa84-4e11-8d02-75535f62e208","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":61378,"visible":true,"origin":"","legend":"","description":"","filename":"Online3.lorenzcurve.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/7a296f3691223027db2c43ed.png"},{"id":99319794,"identity":"1e498d79-2aff-48ae-a943-7d1e4447339c","added_by":"auto","created_at":"2025-12-31 16:37:51","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1030755,"visible":true,"origin":"","legend":"","description":"","filename":"Online4.sensitivityanalysiradar.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/c3f27d1e78981726380e0ce1.png"},{"id":99320000,"identity":"790e0f29-9b0e-4ed4-9f9f-c55d05a11c22","added_by":"auto","created_at":"2025-12-31 16:38:04","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":23615,"visible":true,"origin":"","legend":"","description":"","filename":"Online5.110weightschemes.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/a0240d80be14038bf3296ca4.png"},{"id":99284066,"identity":"7699716d-85ac-4f80-8276-496deab735c2","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":63657,"visible":true,"origin":"","legend":"","description":"","filename":"Online6.Theradarchartof110.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/f45be541ccd7e24e4679503b.png"},{"id":99284075,"identity":"80531cd9-58d0-422b-8402-7259b7660641","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":103653,"visible":true,"origin":"","legend":"","description":"","filename":"Online7.Spearmanheatmap.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/6463636beacd786bf35e2f8d.png"},{"id":99320937,"identity":"169ffcbb-6836-40a2-bd09-5ad3df4bd312","added_by":"auto","created_at":"2025-12-31 16:38:58","extension":"png","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6369,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/41363b65f071994c0a937b73.png"},{"id":99284067,"identity":"347826ad-ba5f-444b-8eee-1bab28020d10","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":27030,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/7dbc5fe3d1c2e389da4aaae8.png"},{"id":99284078,"identity":"4f4e13ce-66fa-4c18-83e1-52b12473e156","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":25579,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/61bc1015a35574a7fcb102bc.png"},{"id":99320670,"identity":"43d74b03-1387-419b-a45b-895a0bf52b0b","added_by":"auto","created_at":"2025-12-31 16:38:51","extension":"png","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":67879,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/9a2f7bf630a9ef90f3cd19a3.png"},{"id":99284074,"identity":"fe3e0fbe-6398-41f1-940e-a8d834b8889c","added_by":"auto","created_at":"2025-12-31 09:07:01","extension":"png","order_by":37,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29042,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/6fea6aecebee0f4ad48029ba.png"},{"id":99318934,"identity":"f5196ba4-50c7-44e9-9fbb-5fb06c78888a","added_by":"auto","created_at":"2025-12-31 16:35:44","extension":"png","order_by":38,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":59344,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/d603975be2506f9ebe7fb0ae.png"},{"id":99320624,"identity":"33b0d03f-1810-4e0a-937e-f705a230fad6","added_by":"auto","created_at":"2025-12-31 16:38:48","extension":"png","order_by":39,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":12477,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/76742358545ffdf4d3e12563.png"},{"id":99318923,"identity":"2b91d9dd-77f0-4c93-ae25-a63cbf96dae2","added_by":"auto","created_at":"2025-12-31 16:35:44","extension":"xml","order_by":40,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":400690,"visible":true,"origin":"","legend":"","description":"","filename":"3ce4bd3afe72472fa08deb80f607ecfe1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/c07da661c00a979822fc4764.xml"},{"id":99318940,"identity":"bb2e2ad6-87b2-4d14-b326-38730a942309","added_by":"auto","created_at":"2025-12-31 16:35:45","extension":"html","order_by":41,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":462138,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/8dab9a08448e8babb096ed89.html"},{"id":101297076,"identity":"51cc3224-c4a5-40f4-845e-8262711a345f","added_by":"auto","created_at":"2026-01-28 09:24:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1008343,"visible":true,"origin":"","legend":"","description":"","filename":"APROBIDHybridDecisionModel.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1_covered_1f03b293-afb5-4bf0-8aad-849542717eea.pdf"},{"id":99320618,"identity":"63b67247-3283-4ba2-8098-521839e4e1c3","added_by":"auto","created_at":"2025-12-31 16:38:48","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":56667,"visible":true,"origin":"","legend":"","description":"","filename":"Summaryofthetablesinthemanuscript.docx","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/67b061b1180e7fdb62f4543e.docx"},{"id":99320642,"identity":"ee8be23e-7569-40d8-b537-91962da085cb","added_by":"auto","created_at":"2025-12-31 16:38:49","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":15359,"visible":true,"origin":"","legend":"","description":"","filename":"attributeweightadjustmentsituations.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8318774/v1/95e5c323b10daa38487c60f7.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"A PROBID Hybrid Decision Model Based on Multi-Valued Neutrosophic Sets and Contact Numbers Integration","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":"Multiple attribute decision making, Multi-valued Neutrosophic Sets, Set Pair Analysis, Contact Numbers, PROBID method","lastPublishedDoi":"10.21203/rs.3.rs-8318774/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8318774/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Multiple attribute decision making (MADM) is a vital part of modern decision science and often faces challenges in representing fuzzy information and maintaining dynamic adaptability under complex uncertain conditions. Although existing studies seek to improve heterogeneous information fusion using fuzzy set theory, research gaps persist in dynamic fuzzy decision mechanisms, reduction of subjective factors, and validation in multi-dimensional scenarios. The classic PROBID method, leveraging an ideal-average distance mechanism, has demonstrated considerable effectiveness across various domains. Yet, its strong sensitivity to attribute weight changes and limited adaptability in static contexts restrict broader applicability. To overcome these issues, this research proposes a hybrid model named multivalued neutrosophic contact numbers-based PROBID (MVCN-PROBID). By integrating the ternary semantic representation of multi-valued neutrosophic numbers (MVNNs) with the identity, discrepancy, and contrary theoretical mechanisms of contact numbers (CNs) in set pair analysis (SPA), a dual-dimensional dynamic evaluation system is established. This synergy within the PROBID framework partially alleviates traditional decision-making bottlenecks in dynamic fuzzy environments. Empirical analysis using two cases, agricultural drone procurement and investment firm selection, shows that MVCN-PROBID produces priority rankings closely matching practical needs. Internal robustness was examined via systematic parameter adjustments, and consistency was verified through multi-method comparative ranking, confirming the model's advantages in stability, applicability, and reliability. This work extends the PROBID method’s theoretical boundaries under a fuzzy mathematics framework, offering a structured solution for MADM in complex settings.","manuscriptTitle":"A PROBID Hybrid Decision Model Based on Multi-Valued Neutrosophic Sets and Contact Numbers Integration","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-31 09:06:56","doi":"10.21203/rs.3.rs-8318774/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"35c048a0-4093-40cb-aaed-631d04069b62","owner":[],"postedDate":"December 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-28T00:38:51+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-31 09:06:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8318774","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8318774","identity":"rs-8318774","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}