The steady states and robustness of fuzzy discrete dynamic systems

DOI

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.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 98
EP  - 105
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.17
DO  - 10.2991/ifsa-eusflat-15.2015.17
ID  - Gavalec2015/06
ER  -