Fuzzy random variables à la Kruse & Meyer and à la Puri & Ralescu: Key differences and coincidences

Abstract

The concept of the so-called fuzzy random variables has been introduced in the literature aiming to model random mechanisms ‘producing’ fuzzy values. However, the best known approaches (namely, the one by Kwakernaak-Kruse and Meyer and the one by Féron-Puri and Ralescu) have been thought to deal with two different situations and, to a great extent, with two different probabilistic and statistical targets. This contribution highlights some of the most remarkable differences and coincidences between the two approaches.