An interactive approach based on a genetic algorithm for a type of quadratic programming problems with fuzzy objective and resources

A type of model of fuzzy quadratic programming problems (FQP) is proposed. It describes the fuzzy objective and resource constraints with different types of membership functions according to different types of fuzzy objective and fuzzy resource constraints in actual production problems. This article develops an inexact approach to solve this type of model of quadratic programming problems with fuzzy objective and resource constraints. Instead of finding an exact optimal solution, we use a Genetic Algorithm (GA) with mutation along the weighted gradient direction to find a family of solutions with acceptable membership degrees. Then by means of the human-computer interaction, the solutions preferred by the DM under different criteria can be achieved.