Abstract
Weak stability of interval orbits of circulant matrices in fuzzy algebra
Highlights
Matrices in fuzzy algebra are useful for expressing applications of fuzzy discrete dynamic systems, graph theory, scheduling, knowledge engineering, cluster analysis, fuzzy systems and for describing diagnosis of technical devices [18], [19], medical diagnosis [15], [16] or fuzzy logic programs [10]
The problem studied in [15] leads to the problem of finding the greatest invariants of the fuzzy system
The aim of this paper is to describe matrices and vectors with inexact data for which there exists a stable orbit, i.e., an orbit with period equal to one, for some matrix and some vector from the given interval vector and interval matrix
Summary
Matrices in fuzzy algebra are useful for expressing applications of fuzzy discrete dynamic systems, graph theory, scheduling, knowledge engineering, cluster analysis, fuzzy systems and for describing diagnosis of technical devices [18], [19], medical diagnosis [15], [16] or fuzzy logic programs [10]. The problem studied in [15] leads to the problem of finding the greatest invariants of the fuzzy system (the greatest eigenvector of the fuzzy matrix corresponding to the greatest eigenvalue). Matrix and vector inputs are rather contained in some intervals than exact values. Considering matrices and vectors with interval coefficients is of great practical importance, see [2], [8], [14]. The main result is concentrated in Theorem 5.1 which gives a necessary and sufficient condition for the weak stability of an interval orbit of circulant matrix which can be checked in O(n2 log n) arithmetic operations
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