Fuzzy stochastic fuzzy time series and its models

In this paper, as an extension of the concept of time series, we will present the definition and models of fuzzy stochastic fuzzy time series (FSFTS), both of whose values and probabilities with which the FSFTS assumes its values are fuzzy sets, and which may not be modeled properly by the concept of time series. To investigate FSFTS, the definition of fuzzy valued probability distributions is considered and discussed. When the FSFTS is time-invariant, several preliminary conclusions are derived.