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.

In this paper, the concept of ¶*-quasiconvexity is introduced by using convexifactors. Mond-Weir-type and Schaible-type duals are associated with a MULTIOBJECTIVE fractional PROGRAMMING problem, and various duality results are established under the assumptions of ¶*-pseudoconvexity and ¶*-quasiconvexity.

In this paper, MULTIOBJECTIVE optimization problems with nondifferentiable quasiconvex functions are considered. We obtain some duality results and a linear representation for the considered problems. Since the well-known strong duality result is not valid for the problems, we present a weaker form of it, named quasi-strong duality result.