Abstract
Interval eigenvectors of circulant matrices in fuzzy algebra
Highlights
Matrices in fuzzy algebra are useful for expressing applications of fuzzy discrete dynamic systems, graph theory, scheduling, medical diagnosis [13], [14] or fuzzy logic programs [7]
The eigenproblem in fuzzy algebra has been studied by many authors
An interval vector X with bounds x, x is defined as follows
Summary
Matrices in fuzzy algebra are useful for expressing applications of fuzzy discrete dynamic systems, graph theory, scheduling, medical diagnosis [13], [14] or fuzzy logic programs [7]. Eigenvector of a fuzzy matrix characterize stable states of the corresponding discrete event systems. Investigation of the fuzzy eigenvectors of a given matrix is of great importance. Interesting results were found in describing the structure of the eigenspace and the algorithms for computing the maximal eigenvector of a given matrix were suggested, see, e.g., [1], [10], [11], [15]. The structure of the eigenspace as a union of intervals of increasing eigenvectors is described in [3]. The structure of the eigenspace for a special case of socalled circulant matrices is described in [5]. The aim of this paper is to describe the interval eigenvectors of circulant matrices.
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