On the power sequence of a fuzzy matrix with convex combination of max-product and max-min operations

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• 作者：Chia-Cheng Liu^a ; ^{liuht@vnu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Yan-Kuen Wu^b ; ¹ ; ^{ykw@vnu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Yung-Yih Lur^a ; ² ; ^{yylur@vnu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Chia-Lun Tsai^c ; ^{s64261992@yahoo.com.tw" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Convex combination of max-product and max-min composition ; Asymptotical p-period ; Nilpotence
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：289
• 期：Complete
• 页码：157-163
• 全文大小：262 K

文摘

In the literature, the powers of a fuzzy matrix with max-min/max-product/max Archimedean t-norm/max t-norm/max-arithmetic mean compositions have been studied. It turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved. In this paper, we consider the powers of a fuzzy matrix with convex combination of max-product and max-min operations. We show that the powers of a fuzzy matrix A with such operations are asymptotical p  -period if and only if the powers of an associated Boolean matrix $\overline{A}$ are p-periodic. Moreover, necessary and sufficient conditions for such a fuzzy matrix to be nilpotent are proposed.