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Based on Einstein operations we define Pythagorean trapezoidal fuzzy Einstein weighted geometric (PTFEWG) operator, Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric (PTFEOWG) operator and Pythagorean trapezoidal fuzzy Einstein hybrid geometric (PTFEHG) operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making. In the last we construct a numerical example for multiple attribute group decision making problem and compare the result with existing method.<\/jats:p>","DOI":"10.3233\/jifs-181329","type":"journal-article","created":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T15:51:59Z","timestamp":1550591519000},"page":"309-324","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["Pythagorean trapezoidal fuzzy geometric aggregation operators based on Einstein operations and their application in 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":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saleem","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Shahzad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Amin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Electronics, University of Engineering and Technology, Taxila, Sub Campus Chakwal, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.","family":"Amin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra KPK, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,2,16]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90215-7"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081070600574353"},{"key":"e_1_3_1_5_2","doi-asserted-by":"crossref","unstructured":"ShakeelM. et al. 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