Two-phase method to solve fuzzy quadratic programming problems

Quadratic programming problems are of up most importance in a variety of relevant practical fields, as e.g., portfolio selection. This work presents and develops an original and novel fuzzy sets based method that solves a class of quadratic programming problems with vagueness in the set of constraints. The method uses two phases to solve fuzzy quadratic programming problems, which eventually can be considered in the portfolio context. In the first phase we parametrize the fuzzy problem in several classical alpha-problems with different cutting levels. In the second phase each of these alpha-problems is solved by using conventional solving techniques. The final fuzzy solution to the former problem can be obtained by integrating all of these particular alpha-solutions. Some illustrative numerical examples illustrating the solution approach are solved and analyzed to show the efficiency of this proposed method.