Theory of Markov systems with fuzzy states

In this paper the theory of fuzzy logic is combined with the theory of Markov systems and the concept of a Markov system with fuzzy states is introduced for the first time. The main objective is to develop a methodology of describing a Markov population system with fuzzy states. This is an effort to deal with the fact that in real applications one is often faced with fuzzy states. This paper investigates the properties of a Markov system with states that have imprecise boundaries. A full description of a nonhomogeneous Markov system with fuzzy states is outlined and the basic parameters of the system are provided. More specifically, the expected population structure of the system is found and given in a closed analytic form and the asymptotic behaviour of the system is provided under the more realistic assumption of a fuzzy set space.