Polynomial form fuzzy numbers and their application in linear programming with fuzzy variables

In this paper, a special class of fuzzy numbers, whose members are called polynomial form fuzzy numbers, is considered. Some properties of its members are presented. Furthermore, linear programming problems with 2-degree polynomial form fuzzy variables are studied. A method using a linear ranking function is proposed to solve the problem. The method generalizes the known methods based on linear ranking functions to solve linear programming problems with trapezoidal variables. To illustrate the method, a transportation problem with fuzzy values of the demands and the supplies is solved and the obtained results are discussed.