A parameterized L2 metric between fuzzy numbers and its parameter interpretation.

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, L2 metrics become especially useful. This paper introduces a new family of generalized L2 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 L2 metrics depends on one parameter. A discussion is provided regarding the interpretation of this parameter which can guide selection of its value in practice.