{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T18:04:41Z","timestamp":1746295481373},"reference-count":23,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2018,8,23]],"date-time":"2018-08-23T00:00:00Z","timestamp":1534982400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773173","71471069"],"award-info":[{"award-number":["61773173","71471069"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2017KFYXJJ178"],"award-info":[{"award-number":["2017KFYXJJ178"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Int Trans Operational Res"],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Weighted scoring rules (WSRs) are usually used for solving problems of group decisions based on individual ordinal preferences. Generally, individuals are influenced by some subjective and objective factors, which lead to the mutability of individual preferences in group decisions. Therefore, while getting optimal solutions, decision makers often need to make qualitative or quantitative sensitivity analyses of their decisions or choices, and to evaluate reliabilities of the solutions. First, by using inclined angles of score vectors, this paper proposes a sensitivity measuring method and some related concepts of group decision using WSRs. Then, a calculation method is presented, and a size of a minimum disturbance group is discussed in depth because this size is also a useful index to evaluate sensitivities or reliabilities of the decisions. Next, we investigate and discuss the sensitivities of WSRs via their weights, and obtain some suggestions about designing WSRs. Finally, we use the sensitivity degree to analyze a controversy of the National Basketball Association Most Valuable Player evaluation. Our measuring methods are: well visualized, scale invariant, commensurable, and calculability.<\/jats:p>","DOI":"10.1111\/itor.12588","type":"journal-article","created":{"date-parts":[[2018,8,23]],"date-time":"2018-08-23T18:45:08Z","timestamp":1535049908000},"page":"959-975","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sensitivity analyses and measurements for group decisions using weighted scoring rules"],"prefix":"10.1111","volume":"28","author":[{"given":"Yong","family":"Zhao","sequence":"first","affiliation":[{"name":"Institute of Systems Engineering School of Automation Huazhong University of Science and Technology  Wuhan 430074 China"},{"name":"Key Laboratory of Image Processing and Intelligent Control of Ministry of Education Huazhong University of Science and Technology  Wuhan 430074 China"}]},{"given":"Fan","family":"Wu","sequence":"additional","affiliation":[{"name":"Institute of Systems Engineering School of Automation Huazhong University of Science and Technology  Wuhan 430074 China"}]},{"given":"Yang","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Systems Engineering School of Automation Huazhong University of Science and Technology  Wuhan 430074 China"},{"name":"Key Laboratory of Image Processing and Intelligent Control of Ministry of Education Huazhong University of Science and Technology  Wuhan 430074 China"}]}],"member":"311","published-online":{"date-parts":[[2018,8,23]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/itor.12373"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00182-012-0332-z"},{"key":"e_1_2_9_4_1","volume-title":"Social Choice and Individual Values","author":"Arrow 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