{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T12:33:49Z","timestamp":1781267629804,"version":"3.54.1"},"reference-count":53,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:00:00Z","timestamp":1565136000000},"content-version":"vor","delay-in-days":218,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61602219"],"award-info":[{"award-number":["61602219"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71740021"],"award-info":[{"award-number":["71740021"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11861034"],"award-info":[{"award-number":["11861034"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11461030"],"award-info":[{"award-number":["11461030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>How to aggregate decision information in heterogeneous multiattribute group decision making (HMAGDM) is vital. The aim of this paper is to develop an approach to aggregating decision data into intuitionistic triangular fuzzy numbers (ITFNs) for heterogeneous MAGDM problems with real numbers (RNs), interval numbers (INs), triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), and triangular intuitionistic fuzzy number (TIFNs). Using the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS) and geometry entropy method, we first present a general approach to aggregating heterogeneous information into ITFNs, which takes the group consistency of experts into account. Based on the collective intuitionistic triangular fuzzy decision matrix and extended TOPSIS, a multiple objective mathematical program is constructed to determine the optimal attribute weights. Subsequently, a new method to solve HMAGDM problems is presented based on the aforementioned discussion. A trustworthy service selection example is provided to verify the practicality and effectiveness of the proposed method.<\/jats:p>","DOI":"10.1155\/2019\/9846582","type":"journal-article","created":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T23:31:20Z","timestamp":1565220680000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Heterogeneous Multiattribute Group Decision\u2010Making Method Based on Intuitionistic Triangular Fuzzy Information"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5321-4550","authenticated-orcid":false,"given":"Jun","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiu-Ying","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6504-9700","authenticated-orcid":false,"given":"Shu-Ping","family":"Wan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3988-6921","authenticated-orcid":false,"given":"De-Yan","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi-Feng","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2019,8,7]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.013"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/cplx.21654"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/cplx.21625"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2014.11.003"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2014.12.014"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2016.03.019"},{"key":"e_1_2_10_7_2","first-page":"1","article-title":"A projection-based approach to software quality evaluation from the users perspectives","author":"Yue C.","year":"2018","journal-title":"International Journal of Machine Learning and Cybernetics"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-019-01473-w"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1080\/0952813X.2019.1572655"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2015.05.016"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2003.11.031"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.08.011"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1108\/K-06-2016-0132"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2017.2694429"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2016.05.046"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2017.09.030"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2018.2865773"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-015-1953-5"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/s13042-017-0650-3"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2016.2610001"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2016.2627050"},{"key":"e_1_2_10_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2006.890678"},{"key":"e_1_2_10_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90205-4"},{"key":"e_1_2_10_25_2","first-page":"803","article-title":"Incentive adaptive trust model based on integrated intuitionistic fuzzy information","volume":"38","author":"Xu J.","year":"2016","journal-title":"Journal of Electronics and Information Technology"},{"key":"e_1_2_10_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-018-3571-5"},{"key":"e_1_2_10_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-03923-6"},{"key":"e_1_2_10_28_2","first-page":"51","article-title":"The comprehensive evaluation of urban environmental quality based on intuitionistic fuzzy set","volume":"38","author":"Yue Z. L.","year":"2008","journal-title":"Mathematics in Practice and Theory"},{"key":"e_1_2_10_29_2","unstructured":"YueZ. L. JiaY. Y. andHuangX. L. Multiple attribute decision making method based on intuitionistic fuzzy set 24 Proceedings of the Second International Conference on Intelligent Information Management Systems and Technology 2007 137\u2013140."},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488509005899"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.11.020"},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.11.108"},{"key":"e_1_2_10_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2012.12.032"},{"key":"e_1_2_10_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.07.007"},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2015.12.045"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-48318-9"},{"key":"e_1_2_10_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2016.09.026"},{"key":"e_1_2_10_38_2","first-page":"88","article-title":"Fuzzy number intuitionistic fuzzy set","volume":"21","author":"Liu F.","year":"2007","journal-title":"Fuzzy Systems and Mathematics"},{"key":"e_1_2_10_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.microrel.2006.01.007"},{"key":"e_1_2_10_40_2","first-page":"104","article-title":"Fuzzy number intuitionistic fuzzy geometric aggregation operators and their application to decision making","volume":"10","author":"Wang X. F.","year":"2008","journal-title":"Control and Decision"},{"key":"e_1_2_10_41_2","first-page":"903","article-title":"Induced fuzzy number intuitionistic fuzzy ordered weighted averaging (I-FIFOWA) operator and its application to group decision making","volume":"7","author":"Wei G. W.","year":"2010","journal-title":"Chinese Journal of Management"},{"key":"e_1_2_10_42_2","first-page":"1964","article-title":"Triangular fuzzy number intuitionistic fuzzy aggregation operators and their application based on interaction","volume":"32","author":"Gao Y.","year":"2012","journal-title":"Systems Engineering Theory & Practice"},{"key":"e_1_2_10_43_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11518-013-5237-2"},{"key":"e_1_2_10_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.01.041"},{"key":"e_1_2_10_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2011.06.044"},{"key":"e_1_2_10_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00402-3"},{"key":"e_1_2_10_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.07.009"},{"key":"e_1_2_10_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.10.006"},{"key":"e_1_2_10_49_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2004.03.008"},{"key":"e_1_2_10_50_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2015.01.054"},{"key":"e_1_2_10_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.05.045"},{"key":"e_1_2_10_52_2","doi-asserted-by":"publisher","DOI":"10.1109\/TR.2018.2869787"},{"key":"e_1_2_10_53_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2018.11.052"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/9846582.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/9846582.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2019\/9846582","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T12:38:53Z","timestamp":1723034333000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2019\/9846582"}},"subtitle":[],"editor":[{"given":"Chittaranjan","family":"Hens","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":53,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1155\/2019\/9846582"],"URL":"https:\/\/doi.org\/10.1155\/2019\/9846582","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"2019-04-04","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-07-16","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-08-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"9846582"}}