On relationships among different types of solutions of fuzzy optimization problems

Article type: Research Article

Authors: Qiu, Dong^* | Xing, Yumei

Affiliations: School of Science, Chongqing University of Posts and Telecommunications, Nanan, Chongqing, P.R. China

Correspondence: [*] Corresponding author. Dong Qiu, School of Science, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, P.R. China. Tel.: +86 15123126186; Fax: +86 23 62471796; E-mail: dongqiumath@163.com.

Abstract: Since fuzzy optimization problems are extensively studied by considering the endpoint functions of level sets of fuzzy-valued objective function with respect to the fuzzy-max order, in this paper, by defining two related partial order relations we establish the complete relationships between the optimal solutions with respect to the fuzzy-max order and the ones with respect to the related partial order relations. These relationships reflect the intrinsic properties of fuzzy optimizations.

Keywords: Fuzzy numbers, fuzzy-max order, fuzzy optimization problems, Pareto optimal

DOI: 10.3233/JIFS-161237

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 889-897, 2017