Abstract
Arrow categories as a suitable categorical and algebraic description of \({\mathcal L}\)-fuzzy relations have been used to specify and describe fuzzy controllers in an abstract manner. The theory of arrow categories has also been extended to include higher-order fuzziness. In this paper we use this theory in order to develop an appropriate description of type-2 fuzzy controllers. An overview of the relational representation of a type-1 fuzzy controller is given before discussing the extension to a type-2 controller. We discuss how to model type reduction, an essential component of any type-2 controller. In addition, we provide a number of examples of general type reducers.
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Winter, M., Jackson, E., Fujiwara, Y. (2014). Type-2 Fuzzy Controllers in Arrow Categories. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2014. Lecture Notes in Computer Science, vol 8428. Springer, Cham. https://doi.org/10.1007/978-3-319-06251-8_18
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DOI: https://doi.org/10.1007/978-3-319-06251-8_18
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