Abstract

Quadratic Programming (QP) represents a special class of nonlinear programming where the objective function is quadratic and constraints are linear. QP can also be viewed as a generalization of linear programming. When real-world applications are considered, vagueness appears in a natural way, and hence it makes perfect sense to think of fuzzy quadratic programming problems. This way of problem modeling is applied in an increasing variety of practical fields. In the first part of the paper, a general history and the approach of fuzzy linear mathematical programming are introduced. In the second part, the fuzzy quadratic mathematical programming is presented. Finally, some techniques and numerical examples using fuzzy quadratic mathematical programming are reviewed.

Keywords: Fuzzy logic, decision making, convex set, fuzzy mathematical optimization, quadratic programming, portfolio selection problem