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A decision making model is proposed by considering the inherent property of IFPRs in this study, where the main novelty comes with the introduction of the concept of additive approximate consistency. First, the consistency definitions of IFPRs are reviewed and the underlying ideas are analyzed. Second, by considering the allocation of the non-determinacy degree of decision makers\u2019 opinions, the novel concept of approximate consistency for IFPRs is proposed. Then the additive approximate consistency of IFPRs is defined and the properties are studied. Third, the priorities of alternatives are derived from IFPRs with additive approximate consistency by considering the effects of the permutations of alternatives and the allocation of the non-determinacy degree. The rankings of alternatives based on real, interval and intuitionistic fuzzy weights are investigated, respectively. Finally, some comparisons are reported by carrying out numerical examples to show the novelty and advantage of the proposed model. It is found that the proposed model can offer various decision schemes due to the allocation of the non-determinacy degree of IFPRs.<\/jats:p>","DOI":"10.3233\/jifs-200200","type":"journal-article","created":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T15:29:09Z","timestamp":1595950149000},"page":"4041-4058","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["Decision making based on intuitionistic fuzzy preference relations with additive approximate consistency"],"prefix":"10.1177","volume":"39","author":[{"given":"Fang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, China"}]},{"given":"Xu","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, China"}]},{"given":"Hui","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, China"}]},{"given":"Hui","family":"Zhao","sequence":"additional","affiliation":[{"name":"China-ASEAN Research Institute, Guangxi University, Nanning, Guangxi, China"}]}],"member":"179","published-online":{"date-parts":[[2020,7,24]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90001-5"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(84)90032-0"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2010.11.007"},{"key":"e_1_3_1_6_2","doi-asserted-by":"crossref","unstructured":"AtanassovK.T. 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