Abstract
In the discrete form of multi-criteria decision-making (MCDM) problems, we are usually confronted with a decision-matrix formed from the information of some alternatives on some criteria. In this study, a new method is proposed for simultaneous evaluation of criteria and alternatives (SECA) in an MCDM problem. For making this type of evaluation, a multi-objective non-linear programming model is formulated. The model is based on maximization of the overall performance of alternatives with consideration of the variation information of decision-matrix within and between criteria. The standard deviation is used to measure the within-criterion, and the correlation is utilized to consider the between-criterion variation information. By solving the multi-objective model, we can determine the overall performance scores of alternatives and the objective weights of criteria simultaneously. To validate the proposed method, a numerical example is used, and three analyses are made. Firstly, we analyse the objective weights determined by the method, secondly, the stability of the performance scores and ranking results are examined, and finally, the ranking results of the proposed method are compared with those of some existing MCDM methods. The results of the analyses show that the proposed method is efficient to deal with MCDM problems.