{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T15:59:10Z","timestamp":1770998350438,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p> Uncertain preference orderings have been widely applied in real world decision making problems as a useful and convenient tool to express preference information. When the number of decision makers is great, the importance degrees of preference interval orderings provided by the decision makers are usually difficult to be determined and may be ignored, which probably lead to the erroneous decision results when the weight information is missing. In order to make full use of information, we define the concepts of probabilistic interval preference ordering set (PIPOS) and probabilistic interval preference ordering element (PIPOE). Then, we give the score and the basic operation laws of PIPOEs, based on which we develop some aggregation operators and the distance measures for PIPOEs. After that, due to the limited cognitions and knowledge of the decision makers, we propose an algorithm to remove the inaccurate information and adjust the probabilities. Furthermore, we put forward the aggregation-based approach and the TOPSIS approach with probabilistic interval preference orderings for multi-criteria group decision making. Finally, in order to illustrate our approaches, we make a detailed case study concerning the infrastructure investment decision making problem on \u201cthe Silk Road Economic Belt and the 21st-Century Maritime Silk Road\u201d (B&amp;R) strategy. <\/jats:p>","DOI":"10.1142\/s0218488517500076","type":"journal-article","created":{"date-parts":[[2017,4,5]],"date-time":"2017-04-05T04:20:26Z","timestamp":1491366026000},"page":"189-212","source":"Crossref","is-referenced-by-count":17,"title":["Probabilistic Interval Reference Ordering Sets in Multi-Criteria Group Decision Making"],"prefix":"10.1142","volume":"25","author":[{"given":"Yue","family":"He","sequence":"first","affiliation":[{"name":"Business School, Sichuan University, Chengdu, Sichuan 610065, China"}]},{"given":"Zeshui","family":"Xu","sequence":"additional","affiliation":[{"name":"Business School, Sichuan University, Chengdu, Sichuan 610065, China"}]},{"given":"Weiling","family":"Jiang","sequence":"additional","affiliation":[{"name":"Business School, Sichuan University, Chengdu, Sichuan 610065, China"}]}],"member":"219","published-online":{"date-parts":[[2017,4,5]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(99)00197-6"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCA.2002.802821"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCA.2010.2052601"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(00)00010-1"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2009.08.001"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2004.01.005"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2009.2039477"},{"key":"p_8","first-page":"97","volume":"4","author":"Xu Z. 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