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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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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