Weighted Optimal Set-Point Aggregation with Linear Diophantine Fuzzy Numbers and Ripple Diffusion for Multi-Attribute Decision-Making

Weighted Optimal Set-Point Aggregation with Linear Diophantine Fuzzy Numbers and Ripple Diffusion for Multi-Attribute Decision-Making | 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 Weighted Optimal Set-Point Aggregation with Linear Diophantine Fuzzy Numbers and Ripple Diffusion for Multi-Attribute Decision-Making Yongjie Guo, Jie Zhang, Borui Ma, Junda Qiu, Jiali Tang, Qi Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9507315/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract A new method called the weighted optimal set-point and Ripple Diffusion Algorithm (WOSP--RDA) is proposed to solve multi-attribute decision-making (MADM) problems under linear Diophantine fuzzy number (LDFN) evaluations. WOSP characterizes the most representative aggregation point of each alternative in the embedded decision space and serves as the optimal aggregation target, while the Ripple Diffusion Algorithm (RDA) is employed to solve the corresponding WOSP model and obtain the final aggregated representation. To enable geometric computation, LDFN assessments are transformed into a four-dimensional real-valued representation, through which weighted attribute information and deviation characteristics can be incorporated into the aggregation process. After obtaining the aggregated results, the final preference ordering is generated by the score function. Moreover, weight-sensitivity analysis under multiple attribute-weight scenarios and outlier-robustness tests under boundary-type perturbations are conducted to examine the stability of the proposed framework. The effectiveness of WOSP--RDA is validated through a benchmark numerical case. Comparative and robustness-related analyses indicate that the proposed method yields discriminative ranking results, preserves good stability under moderate weight changes, and remains robust against localized abnormal evaluations. Overall, WOSP--RDA provides an effective and interpretable aggregation-centered decision framework for LDFN-based MADM problems. linear Diophantine fuzzy numbers multi-attribute decision-making weighted optimal set-point Ripple Diffusion Algorithm robustness analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 11 May, 2026 Reviewers agreed at journal 05 May, 2026 Reviewers agreed at journal 05 May, 2026 Reviewers invited by journal 05 May, 2026 Editor assigned by journal 24 Apr, 2026 Submission checks completed at journal 24 Apr, 2026 First submitted to journal 23 Apr, 2026 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-9507315","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":638906188,"identity":"30f40d1b-9b58-41eb-b4fe-c2b72dd38cae","order_by":0,"name":"Yongjie Guo","email":"","orcid":"","institution":"Jiangsu University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Yongjie","middleName":"","lastName":"Guo","suffix":""},{"id":638906189,"identity":"2d0488a6-44f9-4ea3-b581-e189791ef568","order_by":1,"name":"Jie 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WOSP characterizes the most representative aggregation point of each alternative in the embedded decision space and serves as the optimal aggregation target, while the Ripple Diffusion Algorithm (RDA) is employed to solve the corresponding WOSP model and obtain the final aggregated representation. To enable geometric computation, LDFN assessments are transformed into a four-dimensional real-valued representation, through which weighted attribute information and deviation characteristics can be incorporated into the aggregation process. After obtaining the aggregated results, the final preference ordering is generated by the score function. Moreover, weight-sensitivity analysis under multiple attribute-weight scenarios and outlier-robustness tests under boundary-type perturbations are conducted to examine the stability of the proposed framework. The effectiveness of WOSP--RDA is validated through a benchmark numerical case. 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