The steady states and robustness of fuzzy discrete dynamic systems
- Martin Gavalec, Ján Plavka
- Corresponding Author
- Martin Gavalec
Available Online June 2015.
- https://doi.org/10.2991/ifsa-eusflat-15.2015.17How to use a DOI?
- dynamic system, eigenvector, eigenspace, robustness.
- The steady states of a fuzzy discrete dynamic system correspond to invariants (eigenvectors) of the transition matrix of the system. The structure of the eigenspace of a given fuzzy matrix is considered for various max-T algebras, where T is some triangular norm (Gödel, ukasiewicz, product, drastic). A given transition fuzzy matrix is called (strongly) robust if for every starting vector of a fuzzy discrete dynamic system a multiplication of a power matrix with the starting vector produces a (greatest) eigenvector of the transition matrix. A transition matrix is called weakly robust if the only possibility to arrive at an eigenvector is to start of a fuzzy discrete dynamic system by a vector that is itself an eigenvector. We present characterizations of the eigenspace of a given transition matrix in various max-T algebras. Further results concern the robustness (weak, strong robustness) of a matrix and an interval matrix (matrix with inexact data). Polynomial algorithms for checking the equivalent conditions for (weak, strong) robustness of interval fuzzy matrices are presented.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - CONF AU - Martin Gavalec AU - Ján Plavka PY - 2015/06 DA - 2015/06 TI - The steady states and robustness of fuzzy discrete dynamic systems BT - 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15) PB - Atlantis Press SN - 1951-6851 UR - https://doi.org/10.2991/ifsa-eusflat-15.2015.17 DO - https://doi.org/10.2991/ifsa-eusflat-15.2015.17 ID - Gavalec2015/06 ER -