Finding the fuzzy solutions of a general fully fuzzy linear equation system

Article type: Research Article

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

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

Correspondence: [*] Corresponding author. Hale Gonce Kocken, Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, Istanbul, Turkey. Tel.: +90 212 383 46 05; Fax: +90 212 383 45 90; E-mail: halegk@gmail.com.

Abstract: In this paper, a new algorithm is proposed to find the solutions of a general (square or nonsquare) Fully Fuzzy Linear Equation System (FFLS) with arbitrary trapezoidal fuzzy numbers, i.e. there are no sign restrictions on the variables or the parameters of the system. We introduce the “feasible (strong) fuzzy solution” and “approximate fuzzy solution” concepts, then accordingly “no solution” case of a general FFLS is defined. And a model is proposed by means of a mixed integer programming modelling of “min” and “max” concepts in the multiplication of two arbitrary trapezoidal fuzzy numbers. With the logic of goal programming, the objective function of this model is constructed within the deviation variables. Based on the proposed model, also an algorithm is presented to determine the nature of solutions of a general FFLS. The method is illustrated with some numerical examples. Our numerical results for the examples from the literature are analyzed within some distance functions.

Keywords: General fully fuzzy linear equation system, trapezoidal fuzzy number, fuzzy decision making, mixed integer programming problem, feasible and approximate fuzzy solution

DOI: 10.3233/IFS-151813

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 921-933, 2016