We introduce in this paper a new starting mechanism for multiple-objective linear programming (MOLP) algorithms. This makes it possible to start an algorithm from any solution in objective space. The original problem is first augmented in such a way that a given starting solution is feasible. The augmentation is explicitly or implicitly controlled by one parameter during the search process, whi...

In section 4.1 a new class of higher order (F,ρi, σj)type I functions are introduced for a vector minimization problem. Various known generalized invex functions such as type-I, second order type-I and second order (F,ρi,σj)-type I are particular cases of higher order (F, ρi, σj)-type I functions. This class of functions is used to establish higher order duality results for a nondifferentiable ...

In this paper a multi - objective linear fractional programming problem with the fuzzy variables and vector of fuzzy resources is studied and an algorithm based on a parametric approach is proposed. The proposed solving procedure is based on the parametric approach to find the solution, which provides the decision maker with more complete information in line with reality. The simplicity of the ...

a theorem was recently introduced to establish a relationship betweengoal programming and fuzzy programming for vectormaximum problems.in this short note it is shown that the relationship does not exist underall circumstances. the necessary correction is proposed.

The aim of this study is to investigate multi-dimensional vector variational problems considering data uncertainty in each the objective functional and constraints. We establish robust necessary sufficient efficiency conditions such that any feasible solution could be weakly efficient for under consideration. Emphatically, we present scalar, vector, fractional by using notion a convex functional.

We develop in this article a geometric approach to duality in Multiple Objective Linear Programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.