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.

We develop an algorithm for the solution of Multiobjective linear plus fractional programming problem (MOL+FPP) when some of the constraints are homogeneous in nature. Using homogeneous constraints, first we construct a transformation matrix T which transforms the given problem into another MOL+FPP with fewer constraints. Then, a relationship between these two problems, ensuring that the solution of the original problem can be recovered from the solution of the transformed problem, is established. We repeat this process of transformation until all the homogeneous constraints are removed. Then, we discuss the multi objective programming part, for which fuzzy programming methodology is proposed which works for the minimization of perpendicular distances between two hyper planes (curves) at the optimal points of the objective functions. A suitable membership function is defined with the help of the supremum perpendicular distance. A compromised optimal solution is obtained as a result of the minimization of the The supremum perpendicular distance. The corresponding optimal solution to the original problem is obtained using the transformation matrix. Finally, an example is given to illustrate the proposed model.

The aim of this paper is to establish sequential necessary and sufficient approximate optimality conditions for a constrained convex vector mini-mization problem without any constraint qualifications, characterizing the approximate proper and weak efficient solutions. The constraints are de-scribed by mappings taking values in different preorder vector spaces. Our approach is based essentially on the sequential approximate subdifferential calculus rule for the sums of a finite family of cone convex mappings. To illustrate our main result, an application to Multiobjective fractional pro-gramming problem is given. Finally, we present an important subclass of such problems showing the applicability of the obtained conditions.

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.