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The interval-valued Pythagorean fuzzy sets can easily handle uncertain information more flexibly in the process of decision making. Considering the interrelationship among the input arguments, we extend the Bonferroni mean and the geometric Bonferroni mean to the interval-valued Pythagorean fuzzy environment and solve its practical application problems. First, we develop the interval-valued Pythagorean fuzzy Bonferroni mean and the weighted interval-valued Pythagorean fuzzy Bonferroni mean (WIVPFBM) operators. The properties of these aggregation operators are investigated. Then, we also develop the interval-valued Pythagorean fuzzy geometric Bonferroni mean and the weighted interval-valued Pythagorean fuzzy geometric Bonferroni mean (WIVPFGBM) operators and analyze their properties. Third, we utilize the WIVPFBM and WIVPFGBM operators to fuse the information in the interval-valued Pythagorean fuzzy multicriteria group decision making (IVPFMCGDM) problem, which can obtain much more information in the process of group decision making. With the aid of the linear assignment method, we present its extension and further design a new algorithm for the application of IVPFMCGDM. Finally, an example is given to elaborate our proposed algorithm and validate its excellent performance.
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