A New Family of Metrics in Interval Space and Their Applications to Multicriteria Decision-Making Theory

In this article, we analyze the properties of automorphisms in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}^{2}$</tex-math></inline-formula>. Then, we consider a subclass of these automorphisms which generate a preference order relation and asymmetric distances between bounded and closed intervals. Symmetrizing these distances, we generate a new family of metrics in this space of intervals which depends on the automorphisms. We study its properties and give a characterization that allows us to calculate the distance between intervals in a simple way. We provide many examples to illustrate our results as well as an application in multicriteria decision-making methods with interval data.