Input Control and Rate of Convergence in Fuzzy Non-Homogeneous Markov Systems

Certain aspects of input control of a Non-homogeneous Markov System (NHMS) using fuzzy set theory and fuzzy reasoning are presented in this paper. This is an effort to provide strategies that direct the changes that take place in the population structures of a Fuzzy Non-homogeneous Markov System (F-NHMS) towards a desirable direction. Our goal is to maintain the population structure of the system, (), between two given population structures, and , which is a very important issue in the theory of NHMS. More specifically, we study the aspect of attainability in a F-NHMS and give the input probability vector that achieves our aim. Maintainability is also studied by providing a necessary and sufficient condition such that () lies between the two population structures, for each . Moreover, we prove that under some conditions easily met in practice, the rate of convergence of the sequence of the relative population structures in a F-NHMS is geometric.Finally, an illustrative example is provided