On the resolution of the system of fuzzy Diophantine equations

Article type: Research Article

Authors: Liu, F.-B. | Hu, C.-F.

Affiliations: Department of Mechanical and Automation Engineering, I-Shou University, Taiwan | Department of Industrial Management, I-Shou University, Taiwan

Note: [] Corresponding author. C.-F. Hu, Department of Industrial Management, I-Shou University, Taiwan. Tel.: +886 7 6577711 5530; Fax: +886 7 6577056; Emails: [email protected]. (C.-F. Hu); [email protected]. (F.-B. Liu). This work was supported by the National Science Council (NSC) of R.O.C., under Grant NSC 101-2221-E-214-045.

Abstract: Diophantine equations have played an important role in many applications of optimization and decision making problems. This work considers solving the system of fuzzy Diophantine equations by using the concept of level sets. It is shown that the system of fuzzy Diophantine equations with concave membership functions can be reduced to a regular convex integer programming problem. A modified p-th power Lagrangian method is introduced to deal with the resulting convex integer programming problem as a sequence of linearly constrained convex integer programming problems. The numerical example included not only illustrates the complete solution process but also specifies parameter values used in the actual implementation.

Keywords: Diophantine equations, fuzzy optimization, integer programming

DOI: 10.3233/IFS-130765

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 2, pp. 751-758, 2014