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Fuzzy Automata as Coalgebras

Author

Listed:
  • Ai Liu

    (Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima 739-8511, Japan)

  • Shun Wang

    (School of Mathematical Sciences, Peking University, Beijing 100871, China)

  • Luis Soares Barbosa

    (INL (International Iberian Nanotechnology Laboratory) & INESC TEC, Universidade do Minho, 4704-553 Braga, Portugal)

  • Meng Sun

    (School of Mathematical Sciences, Peking University, Beijing 100871, China)

Abstract

The coalgebraic method is of great significance to research in process algebra, modal logic, object-oriented design and component-based software engineering. In recent years, fuzzy control has been widely used in many fields, such as handwriting recognition and the control of robots or air conditioners. It is then an interesting topic to analyze the behavior of fuzzy automata from a coalgebraic point of view. This paper models different types of fuzzy automata as coalgebras with a monad structure capturing fuzzy behavior. Based on the coalgebraic models, we can define a notion of fuzzy language and consider several versions of bisimulation for fuzzy automata. A group of combinators is defined to compose fuzzy automata of two branches: state transition and output function. A case study illustrates the coalgebraic models proposed and their composition.

Suggested Citation

  • Ai Liu & Shun Wang & Luis Soares Barbosa & Meng Sun, 2021. "Fuzzy Automata as Coalgebras," Mathematics, MDPI, vol. 9(3), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:272-:d:489526
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    References listed on IDEAS

    as
    1. Anupam K. Singh & S. P. Tiwari, 2020. "Fuzzy Regular Languages Based on Residuated Lattice," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 363-376, July.
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