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T-Norm Based Operations in Arrow Categories

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Relational and Algebraic Methods in Computer Science (RAMiCS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11194))

Abstract

Arrow categories have been shown to be a suitable categorical and algebraic framework for L-fuzzy relations. They axiomatize those relations and the usual relational operations such as meet, join, converse, and composition based on the operations given by the lattice of membership values L. However, an important tool when working with and applying fuzzy methods, are meet and composition operators that stem from a certain monoid operation on L (also called a t-norm on L). In this paper we investigate the relational properties of those operations in the abstract setting of arrow categories. In particular, we investigate properties similar to the well-known modular inclusion for regular composition.

M. Winter—The author gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Brock University, St. Catharines, ON, L2S 3A1, Canada

    Michael Winter

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  1. Michael Winter
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Correspondence to Michael Winter .

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Editors and Affiliations

  1. Université Laval, Québec, QC, Canada

    Jules Desharnais

  2. University of Canterbury, Christchurch, New Zealand

    Walter Guttmann

  3. Open Universiteit, Heerlen, The Netherlands

    Stef Joosten

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Winter, M. (2018). T-Norm Based Operations in Arrow Categories. In: Desharnais, J., Guttmann, W., Joosten, S. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2018. Lecture Notes in Computer Science(), vol 11194. Springer, Cham. https://doi.org/10.1007/978-3-030-02149-8_5

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  • DOI: https://doi.org/10.1007/978-3-030-02149-8_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-02148-1

  • Online ISBN: 978-3-030-02149-8

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