The fuzzy primal-dual simplex method is a new and efficient method for solving linear programming problems with fuzzy variables. This algorithm is based on duality results and, similar to the dual simplex method, begins with dual feasibility and proceeds to primal feasibility. An important difference between the dual simplex method and the primal-dual method is that in the primal-dual algorithm, it is not required that the dual feasible solution to be basic. In this paper, we develop the primal-dual simplex method for solving fuzzy Multiobjective linear programming problems. To this end, we utilize the fuzzy weighted sum scalarization method to present a fuzzy single objective optimization problem related to the fuzzy Multiobjective linear programming problem. Then, by partitioning the weights of the weighted sum problem, we generalize the single objective primal-dual algorithm to fuzzy Multiobjective problems. By using the presented algorithm, we can find a set of fuzzy Pareto optimal solutions. Presenting a set of fuzzy Pareto optimal solutions to the decision maker, enables him\her to select the best solution based on his\her preferences. Finally, we apply the proposed algorithm for solving a three-objective optimization problem with fuzzy variables and compare the results with some existing methods.

A Multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval Multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example.

Generally, an engineering design problem has multiple objective functions. Some of these problems can be formulated as Multiobjective geometric programming models. On the other hand, often in the real world, coefficients of the objective functions are not known precisely. Coefficients may be interpreted as fuzzy numbers, which lead to a Multiobjective geometric programming with fuzzy parameters. In this paper, we solve the Multiobjective geometric programming problem with fuzzy parameters by applying a linear ranking function. The linear ranking function is used to compare fuzzy numbers. Finally, a numerical example is given.

In this paper we study fuzzy Multiobjective optimization problems defined for n variables. Based on a new p-dimensional fuzzy stationary-point definition, necessary efficiency conditions are obtained. And we prove that these conditions are also sufficient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general differentiability hypothesis.