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

作者：Sinova Beatriz; Angeles Gil Maria; Teresa Lopez Maria; Van Aelst Stefan

来源：Fuzzy Sets and Systems, 2014, 245: 101-115.

DOI：10.1016/j.fss.2014.01.006

• Fuzzy number
• L-2-metric
• wabl/ldev/rdev representation of fuzzy numbers
• L-2 wabl/ldev/rdev metric
• Weighting parameter

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.

• 出版日期2014-6-16