Two-rank multi-attribute group decision-making with linguistic distribution assessments: An optimization-based integrated approach

Abstract

In real life, two-rank multi-attribute decision-making (MADM), in which all alternatives are divided into two preference-ordered categories, is common. In this paper, we investigate two-rank multi-attribute group decision-making (MAGDM) with linguistic distribution assessments (LDAs). A challenge when tackling such two-rank problems is establishing an LDAs-based two-rank model that maintains a balance between classification accuracy and computational complexity. When neither the threshold nor the number of alternatives within each category is specified in advance, determining individual two-rank results and subsequently aggregating the two-rank results for each decision-maker to resolve conflicts within the group is another challenge. Given these, we aim to propose a novel approach for two-rank MAGDM with LDAs. The main innovations and contributions of this paper are as follows. (a) From the perspective of linguistic scale function (LSF)-based cumulative expectations, we present a new LDAs-based distance measure that exhibits several desirable properties. A new score function for comparing LDAs is subsequently proposed using the new distance and the idea of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). (b) Using the minimum intensity of reversed rankings combined with the misclassification ratio of alternatives as an integrated objective function, we construct two 0-1 integer programming models incorporating constraints associated with the centers and priorities of categories to determine the optimal individual and group two-rank results of alternatives, respectively. (c) We apply our method to two-rank MAGDM associated with short video placement platforms. Comparing the proposed approach with other two-rank MAGDM approaches further demonstrates its effectiveness and rationality.