A parameterized L~2 metric between fuzzy numbers and its parameter interpretation

摘要

When handling fuzzy number data, it is a common practice to make use of a metric to quantify distances between fuzzy numbers. Several metrics have been suggested in the literature for this purpose. When statistically analyzing fuzzy number-valued data, L~2 metrics become especially useful. This paper introduces a new family of generalized L~2 metrics which-take into account key features of the involved fuzzy numbers, namely, a measure of central location and two measures associated with the shape of the fuzzy numbers are used. A crucial property related to these three measures is that necessary and sufficient conditions can be established for them to characterize fuzzy numbers. Furthermore, the family of generalized L~2 metrics depends on one parameter. A discussion is provided regarding the interpretation of this parameter which can guide selection of its value in practice.