Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

The steady states and robustness of fuzzy discrete dynamic systems

Authors
Martin Gavalec, Ján Plavka
Corresponding Author
Martin Gavalec
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.17How to use a DOI?
Keywords
dynamic system, eigenvector, eigenspace, robustness.
Abstract
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.

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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  -