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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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
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