The paradox of monotony of systems by fuzzy probability

Abstract Sometimes failure probabilities of system elements are unknown and they can by presented in a form of fuzzy probabilities. It is well known that the monotony is one of the most important property of system with nonfuzzy probabilities. In this paper it is shown that in general systems with fuzzy failure probabilities do not have the property of monotony. This paradox connects with methods of fuzzy numbers comparison and it can not be considered as a result of real work.