Solving System of Fuzzy Diophantine Equations

This work considers the resolution of the system of fuzzy Diophantine equations. The concept of level sets is adopted to convert this problem into a crisp (traditional) nonlinear integer program. It is shown that the system of fuzzy Diophantine equations with concave membership functions can be reduced to a regular convex integer programming problem. The 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.