The probabilistic weighted averaging distance and its application in group decision making

Purpose - The purpose of this paper is to develop a new decision making method based on distance measures that uses the probabilistic weighted averaging (PWA) operator. The paper introduces the PWA distance (PWAD) operator. It is a new aggregation operator that uses probabilities, weighted averages (WAs) and distance measures. Some of its main properties and particular cases are studied such as the arithmetic weighted Hamming distance and the arithmetic probabilistic Hamming distance. An application in a group decision making problem concerning the selection of investment strategies is also presented. Design/methodology/approach - The paper follows the aggregation operator literature by designing new aggregation operators based on the use of distance measures. Also an application in investment selection is developed. Findings - The PWAD operator is presented. It permits to use distance measures with probabilities and WAs in the same formulation. Moreover, the paper also finds the PWA norm aggregation and implements them in a group decision making problem. Practical implications - The PWAD operator can be applied in a wide range of problems including statistics, economics and engineering. The paper focuses on a multi-person decision making application concerning the selection of the optimal investment strategies. Originality/value - New aggregation operators by using distance measures are presented. Their main advantage is that they unify the WA with the probability. Thus, the paper considers distance measures that include subjective and objective information in the same formulation.