A new approach to estimate the interpolation error of fuzzy data using similarity measures of fuzzy numbers

In this article, new error and similarity indexes to determine the accuracy of interpolation of fuzzy data by cubic spline functions are presented. The measures introduced are based on the similarity measure of fuzzy numbers. Through experimental simulations with different examples, we verify the homogeneity of the error and similarity indexes, which provides a criterion for determining the accuracy of the interpolation method with fuzzy data. The development of a criterion or an error or similarity index represents an important advancement, because of the lack of qualitative measures to estimate the interpolation error using fuzzy numbers in order to compare the results from distinct fuzzy data sets.