Discrete time semi-Markov models with fuzzy state space

In the present paper, the classical semi-Markov model in discrete time is examined under the assumption of a fuzzy state space. The definition of a semi-Markov model with fuzzy states is provided. Basic equations for the interval transition probabilities are given for the homogeneous and non homogeneous case. The definitions and results for the fuzzy model are provided by means of the basic parameters of the classical semi-Markov model.