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Soft Computing: State of the Art Theory and Novel Applications pp 55–70Cite as

Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 291))

Abstract

The aim of this contribution is to elaborate generalized notions of determinant and rank (of a matrix) and to show that the theory of fuzzy relation equations can be investigated with the help of them. We recall the notion of bideterminant of a matrix and investigate its properties in a semilinear space. We introduce three different notions of a rank of a matrix and compare them. Finally, we investigate solvability of a system of fuzzy relation equations in terms of discriminant ranks of its matrices (generalized Kronecker-Capelli theorem).

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Authors and Affiliations

  1. Centre of Excellence IT4Innovations, Division OU, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03, Ostrava, Czech Republic

    Irina Perfilieva & Jiri Kupka

Authors
  1. Irina Perfilieva
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  2. Jiri Kupka
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Corresponding author

Correspondence to Irina Perfilieva .

Editor information

Editors and Affiliations

  1. , Iona College, Machine Intelligence Institute, New Rochelle, 10801, New York, USA

    Ronald R. Yager

  2. Information Technologies of the, Republic of Azerbaijan, Ministry of Communications and, Zarifa Aliyeva str. 33, Baku, AZ1000, Azerbaijan

    Ali M. Abbasov

  3. , Department of Electrical, University of Alberta, ECERF Building W5-023, Edmonton, T6G 2V4, Alberta, Canada

    Marek Z. Reformat

  4. , Department of Information Technology, Azerbaijan Technical University, 25 H.Cavid Ave., Baku, AZ1073, Azerbaijan

    Shahnaz N. Shahbazova

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Perfilieva, I., Kupka, J. (2013). Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations. In: Yager, R., Abbasov, A., Reformat, M., Shahbazova, S. (eds) Soft Computing: State of the Art Theory and Novel Applications. Studies in Fuzziness and Soft Computing, vol 291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34922-5_5

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  • DOI: https://doi.org/10.1007/978-3-642-34922-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34921-8

  • Online ISBN: 978-3-642-34922-5

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