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In this framework, we first establish a relative projection model for two interval linguistic 2-tuples denoted by linguistic term sets with different granularities, and then extend it to multi-granular interval 2-tuple linguistic matrices. Based on this, the similarity measurement between two individual matrices as well as the consensus degree of an individual matrix to a group one is defined. Furthermore, the similarity degrees are applied to determine the importance weights of decision-makers. Besides, a concept of acceptable consensus is introduced to assist in devising an iterative procedure for the purpose of promoting the group consensus and reaching a satisfactory agreement. Finally, to demonstrate the validity and advantages of our proposed framework, an illustrative example which has been examined is furnished.<\/jats:p>","DOI":"10.3233\/jifs-17202","type":"journal-article","created":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T11:24:15Z","timestamp":1499772255000},"page":"1263-1274","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["Consensus-based framework to MCGDM under multi-granular uncertain linguistic environment"],"prefix":"10.1177","volume":"33","author":[{"given":"Xue-Yang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Business, Central South University, Changsha, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian-Qiang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Business, Central South University, Changsha, PR China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,7,11]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2014.994050"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.24200\/sci.2016.3906"},{"key":"e_1_3_2_4_2","article-title":"An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options","author":"Ma Y.X.","year":"2016","unstructured":"MaY.X., WangJ.Q., WangJ. and WuX.H., An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options, Neural Computing and Applications (2016). 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