{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:11:01Z","timestamp":1760242261303,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,16]],"date-time":"2017-03-16T00:00:00Z","timestamp":1489622400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Humanities and Social Science Fund Major Project of Beijing under Grant","award":["15ZDA19"],"award-info":[{"award-number":["15ZDA19"]}]},{"name":"Natural Science Foundation of China under Grant","award":["71671064, 71271083"],"award-info":[{"award-number":["71671064, 71271083"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2015XS33"],"award-info":[{"award-number":["2015XS33"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To characterize the influence of decision makers\u2019 psychological factors on the group decisionprocess, this paper develops a new class of aggregation operators based on reference-dependentutility functions (RUs) in multi-attribute group decision analysis. We consider two types of RUs:S-shaped, representing decision makers who are risk-seeking for relative losses, and non-S-shaped,representing those that are risk-averse for relative losses. Based on these RUs, we establish twonew classes of reference-dependent aggregation operators; we study their properties and showthat their generality covers a number of existing aggregation operators. To determine the optimalweights for these aggregation operators, we construct an attribute deviation weight model and adecision maker (DM) deviation weight model. Furthermore, we develop a new multi-attribute groupdecision-making (MAGDM) approach based on these RU aggregation operators and weight models.Finally, numerical examples are given to illustrate the application of the approach.<\/jats:p>","DOI":"10.3390\/sym9030043","type":"journal-article","created":{"date-parts":[[2017,3,16]],"date-time":"2017-03-16T11:24:28Z","timestamp":1489663468000},"page":"43","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Reference-Dependent Aggregation in Multi-AttributeGroup Decision-Making"],"prefix":"10.3390","volume":"9","author":[{"given":"Jianwei","family":"Gao","sequence":"first","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9353-8875","authenticated-orcid":false,"given":"Huihui","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lu, J., Zhang, G.Q., Ruan, D., and Wu, F.J. 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