Fuzzy valued probability

In this paper the main result is introduction of fuzzy valued probability restricted with respect to probability selectors. In order to treat a highly imprecise probability system, the fuzzy valued probability is defined over the measurable space as a fuzzy valued set function which is not additive in classical sense but it is additive with respect to restricted arithmetics. Some properties and the connection with fuzzy valued measure are discussed. Also, an application in Markov decision process with imprecise information is presented.