A mixed integer programming approach to a square fully fuzzy linear equation

Article type: Research Article

Authors: Ahlatcioglu, Mehmet^{a; *} | Albayrak, Inci^b | Kocken, Hale Gonce^b | Ozkok, Beyza Ahlatcioglu^a

Affiliations: [a] Department of Mathematics, Yildiz Technical University, Davutpasa, Istanbul, Turkey | [b] Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey

Correspondence: [*] Corresponding author. Mehmet Ahlatcioglu, Department of Mathematics, Yildiz Technical University, Davutpasa İstanbul, Turkey. Tel.: +90 2123834310; E-mail: mahlatci@yildiz.edu.tr.

Abstract: In this paper, a new method is proposed to find the feasible (strong) fuzzy solution of a square (n × n) fully fuzzy linear equation system (FFLS) with triangular fuzzy numbers. The main purpose of the proposed method is to remove all the sign restrictions on the parameters and variables. Our method, which is based on the multiplication of two arbitrary triangular fuzzy numbers, converts the FFLS to a mixed integer programming problem. The method is illustrated with numerical examples.

Keywords: Linear equation system, fuzzy number, fuzzy decision making, mixed integer programming

DOI: 10.3233/JIFS-16227

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2009-2015, 2016