Eigenproblems in addition-min algebra¹

Article type: Research Article

Authors: Li, Meng | Wang, Xue-ping^{; *}

Affiliations: School of Mathematical Sciences, Sichuan Normal University, Chengdu, People’s Republic of China

Correspondence: [*] Corresponding author. Xue-ping Wang, Tel.: +86 28 84761502; Fax: +86 28 84761502; E-mail: xpwang1@hotmail.com.

Note: [1] Supported by the National Natural Science Foundation of China (No.12071325)

Abstract: In order to guarantee the downloading quality requirements of users and improve the stability of data transmission in a BitTorrent-like peer-to-peer file sharing system, this article deals with eigenproblems of addition-min algebras. First, it provides a sufficient and necessary condition for a vector being an eigenvector of a given matrix, and then presents an algorithm for finding all the eigenvalues and eigenvectors of a given matrix. It further proposes a sufficient and necessary condition for a vector being a constrained eigenvector of a given matrix and supplies an algorithm for computing all the constrained eigenvectors and eigenvalues of a given matrix. This article finally discusses the supereigenproblem of a given matrix and presents an algorithm for obtaining the maximum constrained supereigenvalue and depicting the feasible region of all the constrained supereigenvectors for a given matrix. It also gives some examples for illustrating the algorithms, respectively.

Keywords: Fuzzy relation inequality, Addition-min composition, Eigenvalue, Eigenvector, Algorithm

DOI: 10.3233/JIFS-234499

Journal: Journal of Intelligent & Fuzzy Systems, vol. 46, no. 1, pp. 91-103, 2024