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PFS is characterized by a positive membership degree, a neutral membership degree, and a negative membership degree, making it more suitable and useful than the intuitionistic fuzzy set (IFS) when dealing with multi-attribute decision making (MADM). The aim of this paper is to develop some aggregation operators for fusing picture fuzzy information. Considering the Muirhead mean (MM) is an aggregation technology which can consider the interrelationship among all aggregated arguments, we extend MM to picture fuzzy context and propose a family of picture fuzzy Muirhead mean operators. In addition, we investigate some properties and special cases of the proposed operators. Further, we develop a novel method to MADM in which the attribute values take the form of picture fuzzy numbers (PFNs). Finally, a numerical example is provided to illustrate the validity of the proposed method.<\/jats:p>","DOI":"10.3233\/jifs-172130","type":"journal-article","created":{"date-parts":[[2018,9,4]],"date-time":"2018-09-04T14:50:38Z","timestamp":1536072638000},"page":"3833-3849","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":21,"title":["A method to multi-attribute decision making with picture fuzzy information based on Muirhead mean"],"prefix":"10.1177","volume":"36","author":[{"given":"Yuan","family":"Xu","sequence":"first","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaopu","family":"Shang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Runtong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weizi","family":"Li","sequence":"additional","affiliation":[{"name":"Informatics Research Centre, Henley Business School, University of Reading, Reading, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuping","family":"Xing","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing Jiaotong University, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,9,3]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2010.01.007"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.10.035"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161640"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90215-7"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2006.890678"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141182"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151809"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141281"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2017.2701324"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.01.036"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21939"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-016-2273-0"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2017.05.016"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488517500350"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-017-0930-3"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2017.03.066"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2016.2634599"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2016.2610001"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12559-017-9453-9"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.01.036"},{"key":"e_1_3_2_23_2","first-page":"75","article-title":"The evidential reasoning approach to medical diagnosis using intuitionistic fuzzy Dempster-Shafer theory","volume":"8","author":"Wang Y.N.","year":"2015","unstructured":"WangY.N., DaiY.P., ChenY.W., MengF.C., The evidential reasoning approach to medical diagnosis using intuitionistic fuzzy Dempster-Shafer theory, Int J Comput Intell Syst 8 (2015), 75\u201394.","journal-title":"Int J Comput Intell Syst"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2014.03.037"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2011.05.004"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2016.01.040"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.11.029"},{"key":"e_1_3_2_28_2","article-title":"Picture fuzzy sets-first results. 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