On bilateral matching between fuzzy sets.

In the paper, we describe the new measure of matching fuzzy sets. The introduced measure of perturbation of one fuzzy set by another fuzzy set is considered instead of commonly used distance between two fuzzy sets. The operations known in the fuzzy set theory are used and the perturbation of one fuzzy set by another fuzzy set is understood as a measure describing changes of the first fuzzy set after adding the second one. Obviously, the opposite case can also be considered wherein the second fuzzy set is perturbed by the first one. In general, the new measure is asymmetric and can provide more information compare to a distance between fuzzy sets. The values of such measures of fuzzy sets’ perturbation are in range between 0 and 1. In this paper several mathematical properties of the measure of fuzzy sets’ perturbation are studied, and the measure of sets’ perturbation is compared to other selected measures. [ABSTRACT FROM AUTHOR]