Reducing the Number of Iterations of the Greatest Eigen Fuzzy Set in Stationary Distribution of Fuzzy Markov Chains

Reducing the Number of Iterations of the Greatest Eigen Fuzzy Set in Stationary Distribution of Fuzzy Markov Chains

A general definition of fuzzy Markov chains over a finite state space is introduced. It has been pointed out that unlike for the classical Markov chains recurrency does not imply ergodicity in the case of the fuzzy Markov chains. However, if a fuzzy Markov chain is ergodic then the rows of its limiting transition matrix are equal to the greatest eigen fuzzy set of the fuzzy relation associated with the chain. We make use of some quasi-random sequences for generating elements of fuzzy transition matrix.