This paper investigates a novel induced ordered weighted averaging (IOWA) distance operator and its application in Pythagorean fuzzy (PF) multiattribute group decision making (MAGDM). First, a new induced aggregated distance operator named the weighted IOWA distance (WIOWAD) operator is developed, which differs from the existing methods in that it considers the dual roles of the order-inducing variables at the same time. In other words, in addition to inducing the order of the arguments, the order-inducing variables of the WIOWAD operator also plays an important role in moderating the associated weight vector. Some useful properties and different families of the WIOWAD are also discussed. Then, an extension of the WIOWAD within the PF situation is presented, thus obtaining the PFWIOWAD operator. Furthermore, a MAGDM method based on the PFWIOWAD is introduced. Finally, the practicality and effectiveness of proposed approach are illustrated in a research and development project selection problem.

In this paper, by unifying the induced ordered weighted averaging (IOWA) and the weighted average, a novel induced aggregation method for intuitionistic fuzzy set is investigated. More specifically, a new intuitionistic fuzzy (IF) induced aggregation operator called weighted intuitionistic fuzzy IOWA weighted average (WIFIOWAWA) operator is introduced. A significant advantage of the WIFIOWAWA operator is that it can eliminate the drawback of the existing operators by the dual roles of its order-inducing variables. In addition, some of its desired properties and families are explored. Furthermore, using the proposed operator, a procedure is developed to solve multiple attribute group decision making problems in the case of IF situation. Finally, an illustrative example is provided to demonstrate the effectiveness and practicality of the developed method.

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.

The aim of this paper is to develop a Pythagorean fuzzy multiattribute group decision making (MAGDM) method based on probabilistic information and the ordered weighted averaging (OWA) approach. The Pythagorean fuzzy probabilistic ordered weighted averaging (PFPOWA) operator is presented. It is a new aggregation operator that considers the probabilities and the OWA in the same formulation. Therefore, it is able to take into account the degree of importance that each concept has in the particular problem considered. Some main properties and different particular cases of the PFPOWA operators are studied. Moreover, a method based on the proposed operator for multiattribute group decision making is put forward. Finally, an example showing analysis of a supplier selection is given to verify the effectiveness and practicability of the proposed method.