Abstract
The system we will look at has the properties: c parallel, independent and identical, servers; finite (M, M > c) system capacity (in the queue and in the servers); and infinite calling source (where the customers come from). We will model the system as a fuzzy, finite, Markov chain. So in this chapter let us first briefly review the needed basic results from crisp (not fuzzy) finite Markov chains. Then we introduce: (1) fuzzy regular, finite, Markov chains; (2) fuzzy absorbing, finite, Markov chains; and (3) other fuzzy Markov chains needed in Chapter 14. Fuzzy regular Markov chains will be used throughout Chapters 5–10 and Chapters 13–17 but fuzzy absorbing, and other fuzzy Markov chains, will be needed only in Chapter 14. The next chapter deals with applying these results on fuzzy regular Markov chains to fuzzy queuing theory. Details on fuzzy Markov chains using fuzzy probabilities may be found in [1] and its application to fuzzy queuing theory is in [2]. Both topics are contained in the book [3].
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References
J.J. Buckley and E. Eslami: Fuzzy Markov Chains: Uncertain Probabilities, MathWare and Soft Computing, 9 (2002), pp. 33–41.
J.J. Buckley and E. Eslami: Uncertain Probabilities I: The Discrete Case, Soft Computing. To appear.
J.J. Buckley: Fuzzy Probabilities: New Approach and Applications, Physica-Verlag, Heidelberg, 2003.
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X. Zheng, K. Reilly and J.J. Buckley: Applying Genetic Algorithms to Fuzzy Probability-Based Web Planning Models, Proceedings ACMSE, Savannah, Ga, 2003, pp. 241–245.
X. Zheng, K. Reilly and J.J. Buckley: Comparing Genetic Algorithms and Exhaustive Methods Used in Optimization Problems for Fuzzy Probability Based Web Planning Models, Proceedings 2003 Int. Conf. on AI, June 23–26, 2003, Las Vegas, Nevada. To appear.
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© 2004 Springer-Verlag Berlin Heidelberg
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Buckley, J.J. (2004). Fuzzy Markov Chains. In: Fuzzy Probabilities and Fuzzy Sets for Web Planning. Studies in Fuzziness and Soft Computing, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36426-9_4
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DOI: https://doi.org/10.1007/978-3-540-36426-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05596-6
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