Abstract
This chapter presents an experimental study about the use of the \(M_n\) generalized mean for the computation of the steady state of a fuzzy Markov chain and its close relationship to the probabilistic sum–product relation. The obtained evidence shows that the \(M_n\) generalized mean leads to obtain a very similar results than its probabilistic counterpart i.e. to have aperiodic limiting distributions and convergence in finite–time unlike the fuzzy \(\max -\min \) relation which mostly leads to non–unique solutions i.e. periodic limiting distributions.
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References
Araiza, R., Xiang, G., Kosheleva, O., Skulj, D.: Under interval and fuzzy uncertainty, symmetric Markov chains are more difficult to predict. In: 2007 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), vol. 26, pp. 526–531. IEEE (2007)
Avrachenkov, K.E., Sanchez, E.: Fuzzy Markov chains: specifities and properties. In: IEEE8th IPMU 2000 Conference, Madrid, Spain, pp. 1851–1856. IEEE (2000)
Avrachenkov, K.E., Sanchez, E.: Fuzzy Markov chains and decision-making. Fuzzy Optim. Decis. Making 1(2), 143–159 (2002)
Figueroa-García, J.C., Kalenatic, D., Lopéz, C.A.: A simulation study on fuzzy Markov chains. Commun. Comput. Inf. Sci. 15(1), 109–117 (2008)
Kalenatic, D., Figueroa-García, J.C., Lopez, C.A.: Scalarization of type-1 fuzzy Markov chains. In: Huang, D.-S., Zhao, Z., Bevilacqua, V., Figueroa, J.C. (eds.) ICIC 2010. LNCS, vol. 6215, pp. 110–117. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14922-1_15
Sanchez, E.: Resolution of eigen fuzzy sets equations. Fuzzy Sets Syst. 1(1), 69–74 (1978)
Sanchez, E.: Eigen fuzzy sets and fuzzy relations. J. Math. Anal. Appl. 81(1), 399–421 (1981)
Sierksma, G.: Limiting polytopes and periodic Markov chains. Linear Multilinear Algebra 46(4), 281–298 (1999). https://doi.org/10.1080/03081089908818622
Thomason, M.: Convergence of powers of a fuzzy matrix. J. Math. Anal. Appl. 57(1), 476–480 (1977)
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Figueroa-García, JC., Neruda, R., Chalco-Cano, Y. (2023). An Experimental Study on Fuzzy Markov Chains Under \(M_n\) Generalized Mean Relation. In: Dick, S., Kreinovich, V., Lingras, P. (eds) Applications of Fuzzy Techniques. NAFIPS 2022. Lecture Notes in Networks and Systems, vol 500. Springer, Cham. https://doi.org/10.1007/978-3-031-16038-7_7
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