Minimal solutions of fuzzy relation inequalities with addition-min composition1

Article type: Research Article

Authors: Mi, Xiao | Wang, Xue-ping^{; *}

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

Correspondence: [*] Corresponding author. Xue-ping Wang, School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, Sichuan, People’s Republic of China. Fax: +86-28-84761393; E-mail: xpwang1@hotmail.com.

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

Abstract: This paper investigates minimal solutions of fuzzy relation inequalities with addition-min composition. It first shows the conditions that an element is a minimal solution of the inequalities, and presents the conditions that the inequalities have a unique minimal solution. It then proves that every solution of the inequalities has a minimal one and proposes an algorithm to searching for a minimal solution with computational complexity O (n2) where n is the number of unknown variables of the inequalities. This paper finally describes all minimal solutions of the inequalities.

Keywords: Fuzzy relation inequality, addition-min composition, minimal solution, algorithm

DOI: 10.3233/JIFS-202590

Journal: Journal of Intelligent & Fuzzy Systems, vol. 41, no. 6, pp. 6089-6095, 2021