A Multiple Criteria Decision Analysis Method for Alternative Assessment Results Obeying a Particular Distribution and Application

A multiple criteria decision analysis (MCDA) problem is studied in this paper, for which the evaluation results obey a particular distribution. First, when solving a multiple criteria decision analysis (MCDA) problem, a grey target decision analysis framework is proposed to determine uncertain parameters and criteria weights. A measurement for comprehensive off-target distance is defined, which includes the undetermined parameters. Second, to satisfy the requirements of a specific distribution (such as a normal distribution) in the assessment results, an optimization model that incorporates the off-target distance constraints is proposed by considering the skewness and kurtosis test method. Third, a particle swarm optimization (PSO) algorithm is extended to solve the proposed model by seeking the appropriate parameters and weights. Fourth, a numerical example is applied to demonstrate the feasibility and application of the proposed method. In the end, the proposed model is extended to other distribution requirements.