A solution algorithm for fuzzy linear programming with piecewise linear membership functions
Fuzzy Sets and Systems
Optimal pacing of trains in freight railroads: model formulation and solution
Operations Research
Lagrangian decomposition for integer nonlinear programming with linear constraints
Mathematical Programming: Series A and B
Solving mixed integer nonlinear programs by outer approximation
Mathematical Programming: Series A and B
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables
Mathematics of Operations Research
Fuzzy Mathematical Programming: Methods and Applications
Fuzzy Mathematical Programming: Methods and Applications
Success Guarantee of Dual Search in Integer Programming: p-th Power Lagrangian Method
Journal of Global Optimization
A Class of Hard Small 0-1 Programs
INFORMS Journal on Computing
Combining Problem Structure with Basis Reduction to Solve a Class of Hard Integer Programs
Mathematics of Operations Research
Hardness of approximating the Minimum Solutions of Linear Diophantine Equations
Theoretical Computer Science
An approximation approach for representing S-shaped membership functions
IEEE Transactions on Fuzzy Systems
Zero duality gap in integer programming: P-norm surrogate constraint method
Operations Research Letters
Non-linear integer programming: Sensitivity analysis for branch and bound
Operations Research Letters
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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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.