On nilpotent fuzzy matrices

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 2004 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 145, pages 287-299 (issn: 0165-0114,

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Authors: Yung-Yih Lur; Chin-Tzong Pang; Sy-Ming Guu;

doi: 10.1016/j.fss.2003.08.006

On nilpotent fuzzy matrices

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Abstract

The authors deal with square matrices over a distributive, bounded lattice [cf. \textit{K. H. Kim, F. W. Roush}, Fuzzy Sets Syst. 4, 293--315 (1980; Zbl 0451.20055); Lin. Alg. Appl. 379, 457--473 (2004; Zbl 1044.15009)]. Nilpotent matrices (over the max-min product) are characterized by spectral radii and by their principal permanents, which improve and generalize some results of \textit{K. L. Zhang} [Fuzzy Sets Syst. 117 (3), 403--406 (2001; Zbl 0971.15008)]. Next, a simultaneous nilpotency of a finite family of matrices is considered and the convergence of mixed powers of nilpotent matrices is examined [cf. \textit{S.-M. Guu, H.-H. Chen, C.-T. Peng}, Fuzzy Sets Syst. 121 (2), 203--207 (2001; Zbl 0994.15017)].

Related Organizations

Yuan Ze University
Taiwan

Keywords

mixed powers, Matrices over special rings (quaternions, finite fields, etc.), max-min product, distributive lattice, nilpotent matrix, matrices over lattices, nilpotent fuzzy matrices, max-min operations, Fuzzy algebraic structures, fuzzy matrices, \(D_{01}\)-lattice

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