Author:

Keywords:

Fuzzy number, L-2-metric, wabl/ldev/rdev representation of fuzzy numbers, L-2 wabl/ldev/rdev metric, Weighting parameter, Science & Technology, Technology, Physical Sciences, Computer Science, Theory & Methods, Mathematics, Applied, Statistics & Probability, Computer Science, Mathematics, LINEAR-REGRESSION MODEL, RANDOM-VARIABLES, BOOTSTRAP TECHNIQUES, EXPECTED VALUE, STRONG LAWS, TIME, INTERVAL, SETS, APPROXIMATION, EXPECTATION, 0101 Pure Mathematics, 0801 Artificial Intelligence and Image Processing, Artificial Intelligence & Image Processing, 4602 Artificial intelligence, 4903 Numerical and computational mathematics, 4904 Pure mathematics

Abstract:

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.