Abstract
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.
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References
Sanchez, E.: Resolution of Eigen Fuzzy Sets Equations. Fuzzy Sets and Systems 1, 69–74 (1978)
Sanchez, E.: Eigen Fuzzy Sets and Fuzzy Relations. J. Math. Anal. Appl. 81, 399–421 (1981)
Avrachenkov, K.E., Sanchez, E.: Fuzzy Markov Chains and Decision-making. Fuzzy Optimization and Decision Making 1, 143–159 (2002)
Araiza, R., Xiang, G., Kosheleva, O., Skulj, D.: Under Interval and Fuzzy Uncertainty, Symmetric Markov Chains Are More Difficult to Predict. In: Proceedings of the IEEE NAFIPS 2007 Conference, vol. 26, pp. 526–531 (2007)
Grimmet, G., Stirzaker, D.: Probability and Random Processes. Oxford University Press, Oxford (2001)
Ross, S.M.: Stochastic Processes. John Wiley and Sons, Chichester (1996)
Ching, W.K., Ng, M.K.: Markov Chains: Models, Algorithms and Applications. Springer, Heidelberg (2006)
Thomason, M.: Convergence of Powers of a Fuzzy Matrix. J. Math. Anal. Appl. 57, 476–480 (1977)
Pang, C.T.: On the Sequence of Consecutive Powers of a Fuzzy Matrix with Maxarchimedean t-norms. Fuzzy Sets and Systems 138, 643–656 (2003)
Gavalec, M.: Computing Orbit Period in Max-min Algebra. Discrete Appl. Math. 100, 49–65 (2000)
Gavalec, M.: Periods of special fuzzy matrices. 16, pp. 47–60. Tatra Mountains Mathematical Publications (1999)
Gavalec, M.: Reaching matrix period is np-complete, vol. 12, pp. 81–88. Tatra Mountains Mathematical Publications (1997)
Avrachenkov, K.E., Sanchez, E.: Fuzzy Markov Chains: Specifities and properties. In: 8th IEEE IPMU 2000 Conference, Madrid, Spain (2000)
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Figueroa García, J.C., Kalenatic, D., Lopez Bello, C.A. (2008). A Simulation Study on Fuzzy Markov Chains. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2008. Communications in Computer and Information Science, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85930-7_15
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DOI: https://doi.org/10.1007/978-3-540-85930-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85929-1
Online ISBN: 978-3-540-85930-7
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