A Concession Equilibrium Solution Method without Weighted Aggregation Operators for Multiattribute Group Decision-Making Problems

This paper introduces a concession equilibrium solution without weighted aggregation operators to multiattribute group decision-making problems (in short MGDMPs). It is of practical significance for all decision-makers to find an optimal solution to MGDMPs or to sort out all candidate solutions to MGDMPs. It is proved that under certain conditions the optimal concession equilibrium solution does exist, and on this important result the optimal concession equilibrium solution is obtained by solving a single objective optimization problem. Moreover, the optimal concession equilibrium solution is equivalent to the robust optimal solution with the group weight aggregation under the worst weight condition. Finally, it is proved that the concession equilibrium solution is equivalent to a complete order, i.e. all candidate alternatives can be sorted by concession equilibrium solution. By defining the triangular fuzzy numbers of target concession value, the optimal concession equilibrium solution or the order of the alternative solutions can be obtained in the range of objective concession ambiguity. Numerical experiment shows that the solution can balance the evaluations of multiattribute group decision makers. This paper provides a new approach to solving multiattribute group decision-making problems.