Abstract
In this paper, we present the induced uncertain Euclidean ordered weighted averaging distance (IUEOWAD) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the Euclidean distance and uncertain information represented by interval numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision-maker by using order-inducing variables in the aggregation of the Euclidean distance. Moreover, it is able to deal with uncertain environments where the information is very imprecise and can be assessed with interval numbers. We study some of its main properties and particular cases such as the uncertain maximum distance, the uncertain minimum distance, the uncertain normalized Euclidean distance (UNED), the uncertain weighted Euclidean distance (UWED) and the uncertain Euclidean ordered weighted averaging distance (UEOWAD) operator. We also apply this aggregation operator to a group decision-making problem regarding the selection new artillery weapons under uncertainty.
Highlights
A wide range of aggregation operators are found in the literature (Beliakov et al 2007; Calvo et al 2002; Torra, Narukawa 2007; Yager et al 2011)
By using the induced uncertain Euclidean ordered weighted averaging distance (IUEOWAD), we obtain a generalization that includes a wide range of uncertain distance measures and uncertain aggregation operators such as the uncertain maximum distance, the uncertain minimum distance, the uncertain normalized Euclidean distance (UNED), the uncertain weighted Euclidean distance (UWED) and the uncertain Euclidean ordered weighted averaging distance (UEOWAD) operator
In order to provide a complete analysis of the different potential results that may occur depending on the interests of the decision makers, we present a wide range of particular cases of IUEOWAD operators such as the uncertain maximum distance, the uncertain minimum distance, the UNED, the UWED, the UEOWAD, the IUEOWAD, the Step-IUEOWAD (k = 2) and the Olympic-uncertain induced Euclidean OWA distance (UIEOWAD)
Summary
A wide range of aggregation operators are found in the literature (Beliakov et al 2007; Calvo et al 2002; Torra, Narukawa 2007; Yager et al 2011). Going a step further, Merigó and Casanovas (2011b) presented the induced Euclidean ordered weighted averaging distance (IEOWAD) operator, which uses the IOWA operator and the Euclidean distance in the same formulation It generalizes the Euclidean ordered weighted averaging distance (EOWAD) operator and provides a parameterized family of distance aggregation operators between the maximum and the minimum distance based on a complex reordering process that reflects the complex attitudinal character of the decision-maker. In decision-making problems, this means that we are considering complex attitudinal characters of the decision-maker that reflect psychological aspects, pressure, utility, and a lot of other aspects This new operator generalizes a wide range of uncertain distance measures and aggregation operators such as the uncertain maximum distance, the uncertain minimum distance, the uncertain normalized Euclidean distance (UNED), the uncertain weighted Euclidean distance (UWED) and the uncertain Euclidean ordered weighted averaging distance (UEOWAD) operator.
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