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.

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.

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.

We present the uncertain OWA distance (UOWAD) operator. It is an extension of the OWA distance (OWAD) operator for uncertain situations in which the available information is given in the form of interval numbers. We study some of their main properties and different particular cases. We further generalize the UOWAD operator by using quasi-arithmetic means, obtaining the quasi-arithmetic UOWAD (Quasi-UOWAD) operator. We also present its application to multiple-attribute group decision-making (MAGDM) problems with interval numbers. Finally, an illustrative numerical example is used to verify the developed approaches.

We introduce a new decision-making approach for dealing with uncertain information and apply it to decision making. We have developed the uncertain induced heavy ordered weighted averaging distance (UIHOWAD) operator. It is a new aggregation operator that generalizes a wide range of uncertain aggregation operators such as the uncertain minimum distance, the uncertain weighted Hamming distance (UWHD), the uncertain OWA distance (UOWAD) operator, and the uncertain heavy OWA distance (UHOWAD) operator. We studied some of its main properties and different particular cases. We also present its applicability in a decision-making problem concerning the selection of investments.

The ordered weighted distance (OWD) measure developed by Xu and Chen having been proved suitable to deal with the situation where the input arguments are represented in exact numerical values. In this paper, we develop some new geometric distance measures with intuitionistic fuzzy information, which are the generalization of some widely used distance measures, including the intuitionistic fuzzy weighted geometric distance (IFWGD) measure, the intuitionistic fuzzy ordered weighted geometric distance (IFOWGD) measure, the intuitionistic fuzzy ordered weighted geometric Hamming distance (IFOWGHD) measure, the intuitionistic fuzzy ordered weighted geometric Euclidean distance (IFOWGED) measure, the intuitionistic fuzzy hybrid weighted geometric distance (IFHWGD) measure. These developed weighted geometric distance measures are very suitable to deal with the situation where the input arguments are represented in intuitionistic fuzzy values. And then, we present a consensus reaching process based on the developed distance measures with intuitionistic fuzzy preference information for group decision making. Finally, we apply the developed approach with a numerical example to group decision making under intuitionistic fuzzy environment.

In this paper, we present a new intuitionistic fuzzy decision-making technique based on similarity measures and the ordered weighted average (OWA) operator. We develop the intuitionistic fuzzy ordered weighted similarity (IFOWS) measure. The main advantage of the IFOWS measure is that it can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Moreover, it provides a very general formulation that includes a wide range of aggregation similarity measures and aggregates the input arguments taking the form of intuitionistic fuzzy values rather than exact numbers. We further develop the interval-valued intuitionistic fuzzy ordered weighted similarity (IVIFOWS) measure. Then we apply the developed similarity measures for consensus analysis in group decision-making with intuitionistic fuzzy information. Finally, a practical case is used to illustrate the developed procedures.