A New Minkowski Distance Based on Induced Aggregation Operators

Abstract

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