This paper discusses the interval-fuzzy quadratic programming problems where the cost coefficient, and constraint coefficient, and right-hand sides, are represented by interval-fuzzy data. Since the parameters are interval-fuzzyvalued, the objective value is interval-fuzzy valued as well. A pair of two-level fuzzy quadratic programs is formulated to calculate the upper bound and lower bound of the objective values of the interval-fuzzy quadratic programming. In each fuzzy quadratic programming problem the parameters in the programming are represented by convex fuzzy numbers. So in each fuzzy quadratic programming problem the derived objective value is a fuzzy number as well. Using Zadeh’s extension principle, a pair of three-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic programming.

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