{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:13:38Z","timestamp":1760242418490,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2017 Special Project of Cultivation and Development of Innovation Base","award":["Z171100002217024"],"award-info":[{"award-number":["Z171100002217024"]}]},{"name":"Program for New Century Excellent Talents from Ministry of Education of the China","award":["NCET-10-0375"],"award-info":[{"award-number":["NCET-10-0375"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["12ZX08"],"award-info":[{"award-number":["12ZX08"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We propose a new class of aggregation operator based on utility function and apply them to group decision-making problem. First of all, based on an optimal deviation model, a new operator called the interval generalized ordered weighted utility multiple averaging (IGOWUMA) operator is proposed, it incorporates the risk attitude of decision-makers (DMs) in the aggregation process. Some desirable properties of the IGOWUMA operator are studied afterward. Subsequently, under the hyperbolic absolute risk aversion (HARA) utility function, another new operator named as interval generalized ordered weighted hyperbolic absolute risk aversion utility multiple averaging-HARA (IGOWUMA-HARA) operator is also defined. Then, we discuss its families and find that it includes a wide range of aggregation operators. To determine the weights of the IGOWUMA-HARA operator, a preemptive nonlinear objective programming model is constructed, which can determine a uniform weighting vector to guarantee the uniform standard comparison between the alternatives and measure their fair competition under the condition of valid comparison between various alternatives. Moreover, a new approach for group decision-making is developed based on the IGOWUMA-HARA operator. Finally, a comparison analysis is carried out to illustrate the superiority of the proposed method and the result implies that our operator is superior to the existing operator.<\/jats:p>","DOI":"10.3390\/sym9070103","type":"journal-article","created":{"date-parts":[[2017,7,3]],"date-time":"2017-07-03T10:27:31Z","timestamp":1499077651000},"page":"103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Interval Generalized Ordered Weighted Utility Multiple Averaging Operators and Their Applications to Group Decision-Making"],"prefix":"10.3390","volume":"9","author":[{"given":"Yunna","family":"Wu","sequence":"first","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"},{"name":"Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Changping, Beijing 102206, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuanbo","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"},{"name":"Beijing Key Laboratory of New Energy and Low-Carbon Development, North China Electric Power University, Changping, Beijing 102206, China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haobo","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, North China Electric Power University, Beijing 102206, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianwei","family":"Gao","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":[[2017,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1016\/j.ejor.2016.09.059","article-title":"An extended todim multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment","volume":"258","author":"Qin","year":"2017","journal-title":"Eur. 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