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First, the Pythagorean fuzzy Choquet integral geometric operator is utilized to aggregate the given decision information to obtain the overall preference value of each alternative by experts. In order to obtain the weight vector of the criteria, an optimization model based on the basic ideal of the traditional gray relational analysis method is established, and the calculation steps for solving Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of gray relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of gray relation to both the positive-ideal solution and negative-ideal solution simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.<\/jats:p>","DOI":"10.1515\/jisys-2018-0099","type":"journal-article","created":{"date-parts":[[2018,9,4]],"date-time":"2018-09-04T05:01:51Z","timestamp":1536037311000},"page":"858-876","source":"Crossref","is-referenced-by-count":9,"title":["Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting"],"prefix":"10.1515","volume":"29","author":[{"given":"Muhammad Sajjad Ali","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics , Hazara University , Mansehra, KPK , Pakistan"}]},{"given":"Saleem","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics , Abdul Wali Khan University , Mardan, KPK , Pakistan"}]},{"given":"Peide","family":"Lui","sequence":"additional","affiliation":[{"name":"School of Management Science and Engineering, Shandong University of Finance and Economics , Jinan , China"}]}],"member":"374","published-online":{"date-parts":[[2018,9,4]]},"reference":[{"key":"2025120523362725954_j_jisys-2018-0099_ref_001","doi-asserted-by":"crossref","unstructured":"K. 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