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Interval Type-2 Fuzzy Markov Chains: Type Reduction

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Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence (ICIC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6839))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

    Juan C. Figueroa-García & Cesar Amilcar Lopez

  2. Universidad de La Sabana, Chía, Colombia

    Dusko Kalenatic

Authors
  1. Juan C. Figueroa-García
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  2. Dusko Kalenatic
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  3. Cesar Amilcar Lopez
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Editor information

Editors and Affiliations

  1. School of Electronics and Information Engineering, Tongji University, 4800 Caoan Road, 201804, Shanghai, China

    De-Shuang Huang

  2. School of Computer and Communication Engineering, Zhengzhou University of Light Industry, No. 5, Dongfeng Road, Jinshui District, 450002, Zhengzhou, Henan, China

    Yong Gan

  3. Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Phalguni Gupta

  4. Department of Biotechnology, Indian Institute of Technology Madras, 600 036, Chennai, Tamilnadu, India

    M. Michael Gromiha

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© 2012 Springer-Verlag Berlin Heidelberg

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Figueroa-García, J.C., Kalenatic, D., Lopez, C.A. (2012). Interval Type-2 Fuzzy Markov Chains: Type Reduction. In: Huang, DS., Gan, Y., Gupta, P., Gromiha, M.M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2011. Lecture Notes in Computer Science(), vol 6839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25944-9_28

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  • DOI: https://doi.org/10.1007/978-3-642-25944-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25943-2

  • Online ISBN: 978-3-642-25944-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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