Fuzzy Markov chains based on the fuzzy transition probability

Markov chains play an important role in the decision analysis. In the practical applications, decision-makers often need to decide in an uncertain condition which the traditional decision theory can´t deal with. In this paper, we combine Markov chains with the fuzzy sets to build a fuzzy Markov chain model using a triangle fuzzy number to denote the transition probability. A method is given to compute the n-step fuzzy transition matrix which is the key point of the model. An algorithm consisting of GA and the hill-climbing algorithm is used to compute the high-order n-step fuzzy transition matrix.