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A Simulation Study on Fuzzy Markov Chains

  • Juan C. Figueroa García
  • Dusko Kalenatic
  • Cesar Amilcar Lopez Bello
Part of the Communications in Computer and Information Science book series (CCIS, volume 15)

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.

Keywords

Markov Chain Stationary Distribution Fuzzy Relation Fuzzy Random Variable Fuzzy Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Juan C. Figueroa García
    • 1
  • Dusko Kalenatic
    • 2
  • Cesar Amilcar Lopez Bello
    • 3
  1. 1.Universidad Distrital Francisco José de CaldasBogotáColombia
  2. 2.Universidad de la Sabana, Chia - Colombia, Universidad Católica de ColombiaBogotáColombia
  3. 3.Universidad Distrital Francisco José de Caldas, Bogotá - Colombia, Universidad de la SabanaChiaColombia

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