As an extension of fuzzy set, a Pythagorean fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision‐making problems. The aim of this paper is to introduce a novel aggregation method for the Pythagorean fuzzy set and analyze possibilities for its application in solving multiple attribute decision‐making problems. More specifically, a new Pythagorean fuzzy aggregation operator called the Pythagorean fuzzy induced ordered weighted averaging‐weighted average (PFIOWAWA) operator is developed. This operator inherits main characteristics of both ordered weighted average operator and induced ordered weighted average to aggregate the Pythagorean fuzzy information. Some of main properties and particular cases of the PFIOWAWA operator are studied. A method based on the proposed operator for multiple attribute group decision making is developed. Finally, we present a numerical example of selection of research and development projects to illustrate applicability of the new approach in a multiple attribute group decision‐making problem.

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This paper develops some new decision making methods for multi-attribute decision making (MADM) problems, in which the attribute weights take the form of crisp numbers, and attribute values take the form of interval-valued intuitionistic fuzzy information. First, based on the Zhenyuan integral, an interval-valued intuitionistic fuzzy Zhenyuan averaging (IVIFZA) operator and an interval-valued intuitionistic fuzzy Zhenyuan geometric (IVIFZG) operator are introduced to facilitate aggregation of interval-valued intuitionistic fuzzy information. The proposed operators allow one to fully consider the importance of different combinations of attributes and, therefore, are highly suitable to handle problems involving inter-dependent or interactive attributes. We further proceed by exploring some desirable properties of the IVIFZA and IVIVZG operators. By employing the proposed operators, a MADM approach based on intervalvalued intuitionistic fuzzy information is proposed. Finally, an illustrative example is presented to verify the developed approach and to demonstrate its practicality and effectiveness.

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