Fuzzy Automata as Coalgebras

Ai Liu, Shun Wang, Luis Soares Barbosa and Meng Sun
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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

Mathematics, 2021, vol. 9, issue 3, 1-21

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.

Keywords: fuzzy automata; coalgebra; fuzzy language; bisimulation; composition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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