On transitivity of generalized fuzzy matrices

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• 作者：Yi-Jia Tan
• 关键词：Algebra ; Generalized fuzzy matrix ; Transitive matrix ; Transitive closure ; Reduction of matrix ; Path algebra
• 刊名：Fuzzy Sets and Systems
• 出版年：2013
• 出版时间：1 January, 2013
• 年：2013
• 卷：210
• 期：Complete
• 页码：69-88
• 全文大小：264 K

文摘

In this paper, generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra. Some elementary properties and characterizations for transitive generalized fuzzy matrices are established and transitivity of powers of a generalized fuzzy matrix is discussed. Also, the transitive closure of a generalized fuzzy matrix is considered and some properties of the transitive closures are obtained. Partial results obtained in this paper generalize the corresponding ones on nilpotent matrices and on matrices with periods.