Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations

  • Irina Perfilieva
  • Jiri Kupka
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 291)


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).


semiring semilinear space residuated lattice bideterminant rank 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Centre of Excellence IT4Innovations, Division OU, Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstravaCzech Republic

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