A Simulation Study on Fuzzy Markov Chains
This paper presents a simulation study on Fuzzy Markov chains to identify some characteristics about their behavior, based on matrix analysis. Through experimental evidence it is observed that most of fuzzy Markov chains does not have an ergodic behavior. So, several sizes of Markov chains are simulated and some statistics are collected.
Two methods for obtaining the Stationary Distribution of a Markov chain are implemented: The Greatest Eigen Fuzzy Set and the Powers of a Fuzzy Matrix. Some convergence theorems and two new definitions for ergodic fuzzy Markov chains are presented and discussed allowing to view this fuzzy stochastic process with more clarity.
KeywordsMarkov Chain Stationary Distribution Fuzzy Relation Fuzzy Random Variable Fuzzy Matrix
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