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We propose the relative consensus degree ILOWA (RCD-ILOWA) operator which uses the relative consensus degree (RCD) variable as the order inducing variable, and the compatibility index ILOWA (CI-ILOWA) operator which uses the compatibility index (CI) variable as the order inducing variable. We also investigate some desired properties of RCD-ILOWA operator and the CI-ILOWA operator which provide theoretic basis for the application of the additive linguistic preference relations in GDM. A general formulation and a nonlinear model to determine experts\u2019 weights and two approaches based on the RCD-ILOWA operator and the CI-ILOWA operator for GDM involving additive linguistic preference relations are developed respectively. A numerical example for comprehensive evaluation is given to illustrate the applications of the new operators.<\/jats:p>","DOI":"10.3233\/ifs-151603","type":"journal-article","created":{"date-parts":[[2015,10,6]],"date-time":"2015-10-06T12:05:52Z","timestamp":1444133152000},"page":"831-843","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Some ILOWA operators and their applications to group decision making with additive linguistic preference relations"],"prefix":"10.1177","volume":"29","author":[{"given":"Ligang","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei, Anhui, China"},{"name":"Signal and Image Processing Institute, Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA"}]},{"given":"Yuanyuan","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, 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