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  • 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).
  • 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). (en)
Title
  • Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations
  • Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations (en)
skos:prefLabel
  • Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations
  • Bideterminant and Generalized Kronecker-Capelli Theorem for Fuzzy Relation Equations (en)
skos:notation
  • RIV/61988987:17610/13:A1301737!RIV13-MSM-17610___
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  • P(ED1.1.00/02.0070)
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  • 63320
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  • RIV/61988987:17610/13:A1301737
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  • semiring; semilinear space; residuated lattice; bideterminant; rank (en)
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  • [117BBB5A8B2E]
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  • Berlin
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  • Soft Computing: State of the Art Theory and Novel Applications
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  • Perfiljeva, Irina
  • Kupka, Jiří
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  • Springer-Verlag
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  • 978-3-642-34921-8
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  • 17610
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