Uniqueness of solutions to fuzzy relational equations regarding Max-av composition and strong regularity of the matrices in Max-av algebra

Jun Xie; Jinlong Yuan; Dongxia Wang; Weili Liu; Chongyang Liu

doi:10.3934/jimo.2017087

Article Contents

2018, Volume 14, Issue 3: 1007-1022. Doi: 10.3934/jimo.2017087

This issue Previous Article On the convergence properties of a smoothing approach for mathematical programs with symmetric cone complementarity constraints Next Article Optimal decisions for a dual-channel supply chain under information asymmetry

Uniqueness of solutions to fuzzy relational equations regarding Max-av composition and strong regularity of the matrices in Max-av algebra

1.
Teaching and Research Office of Mathematics, Department of Basics, PLA Dalian Naval Academy, Dalian 116018, Liaoning, China
2.
Department of Mathematics, Dalian Maritime University, Dalian 116026, Liaoning, China
3.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, PR China
4.
School of Mathematics and Information Science, Shandong Institute of Business and Technology, , Yantai 264005, Shandong, China

* Corresponding author: Jinlong Yuan(yuanjinlong0613@163.com)
* Corresponding author: Jinlong Yuan(yuanjinlong0613@163.com)

Received: March 31, 2016

Revised: November 30, 2016

Early access: August 2017

Published: June 2018

The second author is supported by the China Scholarship Council (Grant No. 201506060121) and Fundamental Research Funds for Central Universities in China. The fifth author is supported by the National Natural Science Foundation of China (Grant No. 11771008) and the Natural Science Foundation of Shandong Province in China (Grant Nos.: ZR2015FM014, ZR2015AL010 and ZR2017MA005).

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Abstract

The problem of solving a fuzzy relational equation plays an important role in fuzzy systems. In this paper, we investigate the uniqueness of solutions of fuzzy relational equations regarding Max-av composition through the relationship between minimal solutions and minimal coverage. A method for verifying the strong regularity of matrices in fuzzy Max-av algebra is proposed in the paper.

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Mathematics Subject Classification: Primary: 34A07; Secondary: 49N60.

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