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Solvability and Stability of Fuzzy Relation Equations

  • Martin Gavalec
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 5)

Abstract

The problem of solvability and the problem of unique solvability of a fuzzy relation equation in an arbitrary max-min algebra are considered and corresponding necessary and sufficient conditions are presented. The results allow to solve both problems by an O(n3) algorithm. Analogous results are presented for the stability and periodicity problem of a fuzzy relation equation. The matrix period of a given square matrix is characterized by periods of non-trivial strongly connected components of associated threshold digraphs. The result enables to compute the matrix period in O(n3) time.

Keywords

Unique Solvability Fuzzy Relation Maximum Solution Discrete Dynamic System Matrix Period 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Martin Gavalec
    • 1
  1. 1.Technical UniversityKošiceSlovakia

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