The Induced Minkowski Ordered Weighted Averaging Distance Operator

The Minkowski distance is a distance measure that generalizes a wide range of other 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 will call it the induced Minkowski OWA distance (IMOWAD). Then, we are able to obtain a wider range of distance measures that includes the Minkowski distance, the Minkowski OWA distance (MOWAD), the induced OWAD (IOWAD), etc. We also present a further generalization that uses quasiarithmetic means. We will call it the QuasiIOWAD operator. We end the paper with a numerical example of the new approach.