A TOPSIS method based on sequential three-way decision

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a method for ranking a limited number of alternatives based on their closeness to an idealized goal. For specific decision-making problems, there may be some alternatives whose merits cannot be judged. Many researchers have proposed some improved ranking methods that enable a more accurate ranking result of the alternatives. However, these methods only serve to rank the alternatives, not to classify them. In order to extend the application scope and decision-making ability of TOPSIS method, this paper designs a three-way TOPSIS method that can handle both classification and ranking of alternatives by introducing sequential three-way decisions. Specifically, we first use the basic principles of TOPSIS method to obtain the Positive Ideal Solution (PIS) and Negative Ideal Solution (NIS) of the alternatives, and design four different three-way TOPSIS models are designed according to the distance measures of each alternative to different ideal solutions. Then we employ sequential three-way decision to divide the alternatives in order to obtain the corresponding decision regions. The alternatives are initially ranked according to the ranking rules of the same decision region, and the final ranking is performed using the ranking rules of different decision regions. Finally, this paper verifies the validity and feasibility of the method through an example about project investment to test the results and comparative analysis.