A Modified TOPSIS Method with Improved Rank Stability and Method Consistency for Multi-criteria Decision Analysis
Open AccessThe TOPSIS method, along with most other MCDA methods, is susceptible to a change in the order of how alternatives are ranked due to the insertion or removal of an alternative to the original MCDA decision matrix. This problem can critically undermine and invalidate the results produced by an MCDA method due to this inconsistency. The problem is referred to as the rank reversal problem. This study sets out to explore and understand the rank reversal problem encountered in the TOPSIS method and shows it to be largely caused by the data normalization technique used for the data aggregation function. It also shows that the severity of the rank reversal problem in the TOPSIS method is dependent on the complexity of the decision matrix. This research also indicates that the method consistency and rank stability of the TOPSIS method are inversely proportional to the complexity of the decision matrix. In order to improve method consistency and rank stability, a new method called the P-TOPSIS is proposed to replace the error-prone TOPSIS method. The P-TOPSIS method is shown to be highly effective against rank reversal problems caused by the addition or removal of non-optimal alternatives. Furthermore, through the simulations it is shown that the P-TOPSIS method can produce very similar results to those produced using the reference methods. In addition, it is found that the P-TOPSIS is not significantly different from the TOPSIS method in terms of method consistency and rank stability when the complexity of the decision matrix is low; however, the P-TOPSIS method is significantly superior to the TOPSIS method as the decision matrix becomes more complex.
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