A New Minkowski Distance Based on Induced Aggregation Operators

The Minkowski distance is a distance measure that generalizes a wide range of distances such as the Hamming and the Euclidean distance. In this paper, we develop a generalization of the Minkowski distance by using the induced ordered weighted averaging (IOWA) operator. We call it the induced Minkowski OWA distance (IMOWAD) or induced generalized OWA distance (IGOWAD) operator. Then, we are able to obtain a wide range of distance measures that includes the Minkowski distance, the Minkowski OWA distance (MOWAD), and the induced OWA distance (IOWAD). We also present a further generalization by using quasi-arithmetic means. We end the paper with a numerical example of the new approach.