Interactive multiple objective programming in optimization of the fully fuzzy quadratic programming problems

In this paper, a quadratic programming (FFQP) problem is considered in which all of the cost coefficients, constraints coefficients, and right hand side of the constraints are characterized by LR fuzzy numbers. Through this paper, the concept of α- level of fuzzy numbers for the objective function, and the order relations on the fuzzy numbers for the constraints are considered. To optimize the interval objective function, the order relations represented by decision maker's preference between intervals are defined by the right limit, the left limit, the center and the width of an interval. The maximization (minimization) problem with interval objective function is converted into a bi- objective problem and then the weighting method is applied for solving it and solves the new problem using the Kuhn- Tucker's necessary conditions. The advantages of the approach, referring to covert the fully fuzzy problem into the bi-objective problem, which is significant and being used in an interactive method for achieving the logical and applicable solutions. Finally, a numerical example is given to illustrate the utility, practically and the efficiency of the method.