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Input Control in Fuzzy Non-Homogeneous Markov Systems

Abstract. 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, N(t), between two given population structures, N1 and N2, which is a very important issue in practical applications. 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 N(t) lies between the two population structures, for each t. Finally, an illustrative example is provided.