Ergodicity of Fuzzy Markov Chains Based on Simulation Using Halton Sequences

Volume 4, Issue 1, pp 380--385 http://dx.doi.org/10.22436/jmcs.04.01.14

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Authors

Behrouz Fathi Vajargah - Department of Statistics, University of Guilan, Rasht, Iran Maryam Gharehdaghi - Department of Statistics, University of Guilan, Rasht, Iran

Abstract

We first introduce fuzzy finite Markov chains and present some of their fundamental properties based on possibility theory. We also bring in a way to convert fuzzy Markov chains to classic Markov chains. In addition, we simulate fuzzy Markov chain using different sizes. It is observed that the most of fuzzy Markov chains not only do have an ergodic behavior, but also they are periodic. Finally, using Halton quasi-random sequence we generate some fuzzy Markov chains which compared to the ones generated by the RAND function of MATLAB. Therefore, we improve the periodicity behavior of fuzzy Markov chains.

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Keywords

• Fuzzy Markov Chains
• Stationary Distribution
• Ergodicity
• Simulation
• Halton Quasi-Random Sequence.

MSC

•  60J10
•  60A86
•  60J22
•  65C40
•  15B15

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