Group Multi-Objective Optimization Under Imprecision and Uncertainty Using a Novel Interval Outranking Approach

This paper deals with group multi-objective optimization problems with imperfect information (imprecision, uncertainty, ill-definition, arbitrariness). Since collective preference, belief, and attitude towards conservatism are ill-defined concepts, the handling of imperfect information is a crucial issue in group decision making. Imperfect knowledge is modeled here using a novel interval-based outranking approach that permits us to handle the levels of conservatism from the group members and its dependence on the set of criteria. We propose two different methods that are appropriate for decision structures in the form of teams and committees. In these structures, there is a special actor (the so-called Supra Decision Maker, SDM) with authority for creating an aggregation of the group members’ preferences, beliefs,and levels of conservatism, and for taking the final collective decision. In the first method, the SDM behaves as an “altruistic dictator”. The SDM creates an “altruistic” aggregation of preferences, beliefs, and levels of conservatism in an outranking model based on interval numbers. This model is then used to identify a final solution that is a best compromise for the SDM, taking into account the interval-based aggregated information from group members. In the second method, each group member uses an interval outranking model to solve an individual optimization problem, and to identify his or her best solution. Based on these individual best solutions, the SDM behaves democratically, searching for a solution that maximizes the measures of group satisfaction and dissatisfaction; the solution is improved through several rounds of consensus-reaching. The potential of both methods is illustrated with a realistically sized example of many-objective project portfolio optimization.