Interval Type-2 Fuzzy Markov Chains: Type Reduction

  • Juan C. Figueroa-García
  • Dusko Kalenatic
  • Cesar Amilcar Lopez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6839)


This paper shows an application of Type-reduction algorithms for computing the steady state of an Interval Type-2 Fuzzy Markov Chain (IT2FM). The IT2FM approach is an extension of the scope of a Type-1 fuzzy markov chain (T1FM) that allows to embed several Type-1 fuzzy sets (T1FS) inside its Footprint of Uncertainty. In this way, a finite state Fuzzy Markov Chain process is defined on an Interval Type-2 Fuzzy environment, finding their limiting properties and its Type-reduced behavior. To do so, two examples are provided.


Stationary Transition Matrix Type Reduction Fuzzy Matrix Fuzzy Matrice Strong Ergodic 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Juan C. Figueroa-García
    • 1
  • Dusko Kalenatic
    • 2
  • Cesar Amilcar Lopez
    • 1
  1. 1.Universidad Distrital Francisco José de CaldasBogotáColombia
  2. 2.Universidad de La SabanaChíaColombia

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