Abstract
Although the classic TOPSIS method is very practical, there may be a problem of rank reversal in the addition, deletion, or replacement of the candidate set, which makes its credibility greatly compromised. Based on the understanding of the classical TOPSIS method, this paper establishes a new improved TOPSIS method called NR-TOPSIS. Firstly, the historical maximum and minimum values of all attribute indicators from a global perspective during the evaluation process are determined. Secondly, according to whether the attributes belong to the benefit attribute or cost attribute, standardization is carried out. And then, in the case where the historical values of attributes are determined, we re-fix the positive ideal solution and the negative ideal solution. At the same time, this paper gives the definition of ranking stable and proves that the NR-TOPSIS proposed satisfies ranking stable, which theoretically guarantees that the rank reversal phenomenon does not exist. Finally, in the verification of examples, the results are consistent with the theoretical analysis, which further support the theoretical analysis. The NR-TOPSIS method overcomes rank reversal, which is not only obviously superior to the classical TOPSIS method but also relatively superior to the R-TOPSIS method which has also overcome rank reversal. It is also superior to other reference methods due to its simple calculation.
Highlights
IntroductionOver the last thirty years, the research on multiple attribute (criteria) decision-making (MADM/MCDM) has become a hot issue in different fields of natural science and social science [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. e technique for order preference by similarity to the ideal solution (TOPSIS) is a useful and powerful method for dealing with MADM problems which is proposed by Hwang and Yoon [17, 18]
Two classical examples will be used to verify the effectiveness of the NR-TOPSIS method presented above. e first simple example comes from the literature [45], which confirms with the theory to verify that the method can avoid the phenomenon of rank reversal. e second example is used to illustrate the comprehensive effectiveness of the NR-TOPSIS method
The classical TOPSIS method is not credible because of the possible phenomenon of rank reversal, so it is necessary to carry out theoretical research and process improvement of TOPSIS to resist rank reversal
Summary
Over the last thirty years, the research on multiple attribute (criteria) decision-making (MADM/MCDM) has become a hot issue in different fields of natural science and social science [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. e technique for order preference by similarity to the ideal solution (TOPSIS) is a useful and powerful method for dealing with MADM problems which is proposed by Hwang and Yoon [17, 18]. TOPSIS is a general method for solving MADM problems, which takes into account both positive and negative ideal solutions. Ese hybrid methods make full use of the advantages of the TOPSIS method, which can quantitatively characterize the difference between the alternatives and the positive and negative ideal solutions. They do not discuss the fact that if the TOPSIS method has a reversal of order, the credibility of the hybrid approach will be severely reduced. When the decision-making object changes on the original basis, especially increasing or reducing the evaluation object or replacing a certain evaluation object, the traditional TOPSIS method often has the phenomenon of rank reversal. Many MADM methods have the problem of rank reversal, such as analytic hierarchy
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