Li, Jianxin Periodicity of powers of fuzzy matrices (finite fuzzy relations). (English) Zbl 0760.15012 Fuzzy Sets Syst. 48, No. 3, 365-369 (1992). The author examines the semigroup of powers of a finite fuzzy relation [cf. M. G. Thomason, J. Math. Anal. Appl. 57, 476-480 (1977; Zbl 0345.15007)]. He presents estimations and an algorithm for the determination of the index and the period of this semigroup. Further results are given in the author’s paper [An upper bound of indices of finite fuzzy relations, Fuzzy Sets Syst. 49, 317-321 (1992)]. Reviewer: J.Drewniak (Katowice) Cited in 3 ReviewsCited in 14 Documents MSC: 15B33 Matrices over special rings (quaternions, finite fields, etc.) 03E72 Theory of fuzzy sets, etc. 15B57 Hermitian, skew-Hermitian, and related matrices 20M14 Commutative semigroups Keywords:matrix power; matrix semigroup; convergence of powers; oscillation of powers; fuzzy relation; index; period PDF BibTeX XML Cite \textit{J. Li}, Fuzzy Sets Syst. 48, No. 3, 365--369 (1992; Zbl 0760.15012) Full Text: DOI References: [1] Dubois, D.; Prade, H., Fuzzy sets and systems, (1980), Academic Press New York [2] Hashimoto, H., Convergence of powers of a fuzzy transitive matrix, Fuzzy sets and systems, 9, 153-160, (1983) · Zbl 0509.15009 [3] Kolodziejczyk, W., Convergence of powers of s-transitive fuzzy matrices, Fuzzy sets and systems, 26, 127-130, (1988) · Zbl 0647.15010 [4] Kim, K.H.; Roush, F.W., Generalized fuzzy matrix, Fuzzy sets and systems, 4, 293-316, (1980) [5] Kandel, A., Fuzzy mathematical techniques with applications, (1986), Addison-Wesley Reading, MA [6] Jian-Xin, Li, Some results on the nilpotent fuzzy matrices, Fuzzy systems and mathematics, 1, 52-55, (1989), (in Chinese) [7] Li Jian-Xin, Convergence of powers of controllable fuzzy matrices, Chinese Journal of Mathematics, to appear. · Zbl 0826.15020 [8] Rosen, K.H., Elementary number theory and its applications, (1984), Addison-Wesley Reading, MA · Zbl 0546.10001 [9] Dan, Sa; Wangming, Wu, Graphics characteristics of power convergence of fuzzy matrix, Fuzzy mathematics, 1, 1-4, (1987) [10] Thomason, M.G., Convergence of powers of a fuzzy matrix, J. math. anal. appl., 57, 476-480, (1977) · Zbl 0345.15007 [11] Reiying, Zhu, Convergence of powers of a fuzzy symmetric matrix, Fuzzy mathematics, 3, 45-49, (1984) · Zbl 0575.15010 [12] Zadeh, L.A., Fuzzy sets, Inform. and control., 8, 338-353, (1965) · Zbl 0139.24606 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.