Using the Probabilistic Weighted Average in Decision Making with Distance Measures

We develop a new decision making method based on distance measures that uses the probabilistic weighted averaging (PWA) operator. The PWA operator is an aggregation operator that unifies the weighted average and the probability in the same formulation and considering the degree of importance that each concept has in the aggregation. We introduce the probabilistic weighted averaging distance (PWAD) operator. It is a new aggregation operator that uses probabilities, weighted averages and distance measures. We study some of its main properties and particular cases such as the arithmetic weighted Hamming distance and the arithmetic probabilistic Hamming distance. We also develop an application in a decision making problem concerning the selection of investment strategies.