Rationality criterion of comprehensive evaluation method

Up to now, there is no recognized criterion to evaluate the rationality of the methods for comprehensive evaluation. By comparing with the results of comprehensive evaluation of the same kind objects, and from the perspective of multi-objective optimization, it can be found that the integrated function of the comprehensive evaluation is none other than the comprehensive single objective function of the multiobjective optimization problem. The factors involved in the comprehensive evaluation are just equivalent to the objectives of the multiobjective optimization problem. The region limited by factors states is just the feasible region. Based on this point of view, a rationality criterion to evaluate a comprehensive evaluation method is proposed in this paper. The criterion demands that optimal solution of the integrated function in the feasible region must be Pareto optimal. The criterion thus theoretically gives a reasonable explanation for the properties that are required in some evaluation functions and operators appeared on all kinds of literatures and references. Finally, the rationalities of fuzzy comprehensive evaluation methods are discussed and compared with each other.