Random fuzzy sets

Abstract

Statistical models for observations which are numbers or vectors are random variables and random vectors, respectively. Similarly, if the observations are subsets of some set, then appropriate statistical models are random sets of that set. Motivated by the desire to generalize numbers to fuzzy numbers and random closed sets to fuzzy sets, we establish here a reasonable concept of random fuzzy sets which can be used in statistical inference with fuzzy data. © Springer-Verlag Berlin Heidelberg 2006.