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Pythagorean fuzzy set, an extension of the intuitionistic fuzzy set which relax the condition of sum of their membership function to square sum of its non-membership functions is less than one. In this paper, we proposed some operational rules based on PTFNs and verified their some properties. we developed some aggregation operators to use the decision information represented by PTFNS, including the Pythagorean trapezoidal fuzzy weighted averaging (PTFWA) operator, Pythagorean trapezoidal fuzzy ordered weighted averaging (PTFOWA) operator and Pythagorean trapezoidal fuzzy hybrid averaging (PTFHA) operator. Furthermore, we proved their some desirable properties. Based on the (PTFWA) operator, the PTFOWA operator and the PTFHA operator, we presented some new method to deal with the multi-attribute group decision making (MAGDM) problems under the Pythagorean trapezoidal fuzzy environment. Finally, we used some practical example to illustrate the validity and feasibility of the proposed methods by comparing with other methods.<\/jats:p>","DOI":"10.3233\/jifs-17238","type":"journal-article","created":{"date-parts":[[2018,8,24]],"date-time":"2018-08-24T13:53:40Z","timestamp":1535118820000},"page":"1899-1915","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":26,"title":["Averaging aggregation operators with pythagorean trapezoidal fuzzy numbers and their application to group decision making"],"prefix":"10.1177","volume":"36","author":[{"given":"M.","family":"Shakeel","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hazara University Mansehra, KPK, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Abduulah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University Mardan, KPK, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Shahzad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University Mansehra, KPK, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, University of Engineering and Technology Taxila Sub Campus, Chakwal, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"N.","family":"Siddiqui","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, University of Engineering and Technology Taxila, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2018,8,22]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"crossref","unstructured":"AtanassovK.T. 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