On the resolution of the system of fuzzy Diophantine equations

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.