On fuzzy solutions of the nonsquare fully fuzzy linear equation system with arbitrary triangular fuzzy numbers

Article type: Research Article

Authors: Albayrak, Inci^{; *}

Affiliations: Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey

Correspondence: [*] Corresponding author. Inci Albayrak, Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey. Tel.: +905054112181; Fax: +902123834590; E-mail: ibayrak@yildiz.edu.tr.

Abstract: In this paper, Fully Fuzzy Linear Equation System (FFLS) that all parameters and variables are represented by triangular fuzzy numbers is discussed. FFLS has many important applications to branches of science, engineering and other disciplines. The objective of this paper is to find the feasible (strong) and approximate solution with a proposed method based on a mixed integer modeling of the nonsquare FFLS by removing all restrictions on the parameters and variables. The method is illustrated with numerical examples. Results of the numerical examples show that this method has the ability to generate a feasible (strong) and an approximate fuzzy solution and also to indicate no solution case of a nonsquare or square FFLS.

Keywords: Nonsquare fully fuzzy linear equation system, triangular fuzzy number, mixed integer programming

DOI: 10.3233/JIFS-17774

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3929-3938, 2017