ScholarLens Back to search
2011•International Journal of Computational Intelligence SystemsOpen access

A New Minkowski Distance Based on Induced Aggregation Operators

José M. Merigó, Montserrat Casanovas

Open full text 90 citations

Abstract

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.

About this research paper

What this paper is about

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.

Why it matters

OpenAlex reports 90 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

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.

Key concepts: Minkowski distance, Minkowski space, Hamming distance, Generalization, Distance measures, Mathematics, Euclidean distance, Range (aeronautics)

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
A New Minkowski Distance Based on Induced Aggregation Operators — Research Paper | ScholarLens