Quadratic programming with interval fuzzy parameters

This paper discusses the intervalfuzzy quadratic programming problems where the cost coefficient, and constraint coefficient, and right-hand sides, are represented byinterval-fuzzy data. Since the parameters are interval-fuzzy-valued, the objective value is interval-fuzzy valued as well. A pair of twolevelfuzzy 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 ineach fuzzy quadratic programming problem the derived objective value is a fuzzy number as well. Using Zadeh’s extension principle, apair of three-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of thefuzzy quadratic programming.

Keywords:

Membership function , quadratic programming , interval fuzzy