{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:59:01Z","timestamp":1760147941299,"version":"build-2065373602"},"reference-count":67,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,15]],"date-time":"2023-03-15T00:00:00Z","timestamp":1678838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of China","award":["72171123","72171149"],"award-info":[{"award-number":["72171123","72171149"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Due to the complexity and uncertainty of decision-making circumstances, it is difficult to provide an accurate compensation cost in strategic weight manipulation, making the compensation cost uncertain. Simultaneously, the change in the attribute weight is also accompanied by risk, which brings a greater challenge to manipulators\u2019 decision making. However, few studies have investigated the risk aversion behavior of manipulators in uncertain circumstances. To address this research gap, a robust risk strategic weight manipulation approach is proposed in this paper. Firstly, mean-variance theory (MVT) was used to characterize manipulators\u2019 risk preference behavior, and a risk strategic weight manipulation model was constructed. Secondly, the novel robust risk strategic weight manipulation model was developed based on the uncertainty caused by the estimation error of the mean and covariance matrix of the unit compensation cost. Finally, a case of emergency facility location was studied to verify the feasibility and effectiveness of the proposed method. The results of the sensitivity analysis and comparative analysis show that the proposed method can more accurately reflect manipulators\u2019 risk preference behavior than the deterministic model. Meanwhile, some interesting conclusions are revealed.<\/jats:p>","DOI":"10.3390\/systems11030151","type":"journal-article","created":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T02:40:11Z","timestamp":1678934411000},"page":"151","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Strategic Weight Manipulation Model in Uncertain Environment: A Robust Risk Optimization Approach"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4746-270X","authenticated-orcid":false,"given":"Shaojian","family":"Qu","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lulu","family":"Zuo","sequence":"additional","affiliation":[{"name":"Business School, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Business School, University of Shanghai for Science and Technology, Shanghai 200093, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110751","DOI":"10.1016\/j.oceaneng.2022.110751","article-title":"Comparison of multicriteria analysis techniques for decision making on floating offshore wind farms site selection","volume":"248","author":"Loughney","year":"2022","journal-title":"Ocean Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"125816","DOI":"10.1016\/j.amc.2020.125816","article-title":"Multi-attribute decision making: An innovative method based on the dynamic credibility of experts","volume":"393","author":"Zhang","year":"2021","journal-title":"Appl. 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