Geometric characterizations of a class of joint efficient solutions in group multicriteria decision making

Group multiple criteria decision making (GMCDM) is an overlapping field of group decision making and multiple criteria decision making. With the help of efficient sets of alternatives, concepts of a class of joint efficient solutions and Karush–Kuhn–Tucker optimality conditions of these solutions are both presented for the GMCDM. In this paper, the geometric characterizations of the joint efficient solutions are studied, and some basic necessary conditions and sufficient conditions are obtained.