{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T17:03:29Z","timestamp":1769879009806,"version":"3.49.0"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,15]],"date-time":"2020-04-15T00:00:00Z","timestamp":1586908800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Social Science Foundation of China","award":["Grant No. 14ZDB151"],"award-info":[{"award-number":["Grant No. 14ZDB151"]}]},{"name":"National Social Science Foundation of China","award":["Grant No. 18CJY018"],"award-info":[{"award-number":["Grant No. 18CJY018"]}]},{"name":"National Social Science Foundation of China","award":["Grant No. 16AZD018"],"award-info":[{"award-number":["Grant No. 16AZD018"]}]},{"name":"International Postdoctoral Exchange Fellowship Program","award":["Grant No.20190023"],"award-info":[{"award-number":["Grant No.20190023"]}]},{"name":"National Special Science Foundation for Postdoctoral Scientists of China","award":["Grant No. 2018T110708"],"award-info":[{"award-number":["Grant No. 2018T110708"]}]},{"name":"National Science Foundation for Postdoctoral Scientists of China","award":["Grant No. 2017M610446"],"award-info":[{"award-number":["Grant No. 2017M610446"]}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["Grant No. 2016YFC1402000"],"award-info":[{"award-number":["Grant No. 2016YFC1402000"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Foundation for Postdoctoral Scientists of Qingdao City, China","award":["Grant No. 24"],"award-info":[{"award-number":["Grant No. 24"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Considering the characteristics such as fuzziness and greyness in real decision-making, the interval grey triangular fuzzy number is easy to express fuzzy and grey information simultaneously. And the partition Bonferroni mean (PBM) operator has the ability to calculate the interrelationship among the attributes. In this study, we combine the PBM operator into the interval grey triangular fuzzy numbers to increase the applicable scope of PBM operators. First of all, we introduced the definition, properties, expectation, and distance of the interval grey triangular fuzzy numbers, and then we proposed the interval grey triangular fuzzy numbers partitioned Bonferroni mean (IGTFPBM) and the interval grey triangular fuzzy numbers weighted partitioned Bonferroni mean (IGTFWPBM), the adjusting of parameters in the operator can bring symmetry effect to the evaluation results. After that, a novel method based on IGTFWPBM is developed for solving the grey fuzzy multiple attribute group decision-making (GFMAGDM) problems. Finally, we give an example to expound the practicability and superiority of this method.<\/jats:p>","DOI":"10.3390\/sym12040628","type":"journal-article","created":{"date-parts":[[2020,4,16]],"date-time":"2020-04-16T05:15:41Z","timestamp":1587014141000},"page":"628","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Grey Fuzzy Multiple Attribute Group Decision-Making Methods Based on Interval Grey Triangular Fuzzy Numbers Partitioned Bonferroni Mean"],"prefix":"10.3390","volume":"12","author":[{"given":"Kedong","family":"Yin","sequence":"first","affiliation":[{"name":"School of Economics, Ocean University of China, Qingdao 266100, China"},{"name":"Ocean Development Research Institute, Major Research Base of Humanities and Social Sciences of Ministry of Education, Ocean University of China, Qingdao 266100, China"},{"name":"College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, China"}]},{"given":"Benshuo","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Economics, Ocean University of China, Qingdao 266100, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1231-3528","authenticated-orcid":false,"given":"Xue","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Economics, Ocean University of China, Qingdao 266100, China"},{"name":"Ocean Development Research Institute, Major Research Base of Humanities and Social Sciences of Ministry of Education, Ocean University of China, Qingdao 266100, China"},{"name":"College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, China"},{"name":"Institute for the Oceans and Fisheries, University of British Columbia, 2202 Main Mall, Vancouver, BC V6T 1Z4, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, J., Gao, H., Wei, G., and Wei, Y. 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