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First, the attribute weights are obtained using the truth favorite relative expected value, and the distance measure defined using the cosine similarity measure. Next, a proposed trapezoidal fuzzy neutrosophic number ordered weighted arithmetic averaging (TrFNNOWAA) operator and a proposed trapezoidal fuzzy neutrosophic number hybrid weighted arithmetic averaging (TrFNNHWAA) operator are used to aggregate the trapezoidal fuzzy neutrosophic information. Then, the score and accuracy functions of a trapezoidal neutrosophic number are used to rank the alternatives and obtain the best alternative in a trapezoidal fuzzy neutrosophic environment. In addition, an extended TOPSIS method is also proposed to deal with trapezoidal fuzzy neutrosophic information. An illustrative example and sensitivity analysis demonstrate the applicability and effectiveness of the proposed group decision making methods.<\/jats:p>","DOI":"10.3233\/jifs-161984","type":"journal-article","created":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T11:22:08Z","timestamp":1499772128000},"page":"2547-2564","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":17,"title":["Multiple attribute group decision making methods based on trapezoidal fuzzy neutrosophic numbers"],"prefix":"10.1177","volume":"33","author":[{"given":"Ruipu","family":"Tan","sequence":"first","affiliation":[{"name":"School of Economics and Management, Fuzhou University, Fuzhou, China"},{"name":"College of Electronics and Information Science, Fujian Jiangxia University, Fuzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wende","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Information Management, Fuzhou University, Fuzhou, China"},{"name":"Information Construction Office, Fuzhou University, Fuzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,7,8]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-015-1891-2"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_3_2_5_2","volume-title":"A unifying field in logics. 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