For a group multiobjective programming problem, the stability results of a class of joint cone weakly efficient solution sets in the sense of upper semi-continuance were obtained with respect to the decision making variable perturbation and objective order perturbation respectively.

The weak duality theorem, the basic duality theorem, the direct duality theorem and the adverse duality theorem under the means of the joint weak efficient solution are derived.

This paper is concerned with Mond-Weir type duality about the joint efficient solution in group multiobjective programming, which contains the unsymmetrical objective functions and constraints.

In [1], the concept of a class joint efficient solution to group multiobjective decision making problem is introduced, as well as some optimality necessary conditions for these solutions.

For group multiobjective decision making problems, a class of joint efficient solutions is introduced by means of efficient numbers of alternatives and the optimality necessary conditions are established in the paper [1].

In this paper, the relation between connectedness of the cone-efficient solution set of multiobjective optimization problem and connectedness of the corresponding cone-efficient point set is considered, and a sufficient and necessary condition is provided.