Interval-valued Pythagorean fuzzy GRA method for multiple-attribute decision making with incomplete weight information

In this paper, the concept of multiple-attribute group decision-making (MAGDM) problems with interval-valued Pythagorean fuzzy information is developed, in which the attribute values are interval-valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval-valued Pythagorean fuzzy sets is the generalization of interval-valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval-valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval-valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval-valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval-valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval-valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive-ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness.