A novel approach for ranking intuitionistic fuzzy numbers and its application to decision making

Ranking intuitionistic fuzzy numbers is an important issue in the practical application of intuitionistic fuzzy sets. Many scholars rank intuitionistic fuzzy numbers by defining different measures. These measures do not comprehensively consider the fuzzy semantics expressed by membership degree, nonmembership degree, and hesitancy degree. As a result, the ranking results are often counterintuitive, such as the indifference problems, the non-robustness problems, etc. In this paper, according to geometrical representation, a novel measure for intuitionistic fuzzy numbers is defined, which is called the ideal measure. After that, a new ranking approach is proposed. Its proved that the ideal measure satisfies the properties of weak admissibility, membership degree robustness, nonmembership degree robustness, and determinism. A numerical example is applied to illustrate the effectiveness and feasibility of this method. Finally, using the presented approach, the optimal alternative can be acquired in multi-attribute decision-making problems. Comparison analysis shows that the ideal measure is more effective and simple than other existing methods.

Automated summary

Ranking intuitionistic fuzzy numbers is crucial in practical applications of intuitionistic fuzzy sets. Existing measures for ranking these numbers do not comprehensively consider the fuzzy semantics expressed by membership degree, non-membership degree, and hesitancy degree, resulting in counterintuitive ranking results. This paper proposes a novel measure called the ideal measure and a new ranking approach based on geometric representation. The ideal measure is proven to satisfy properties such as weak admissibility, membership degree robustness, non-membership degree robustness, and determinism. A numerical example demonstrates the effectiveness and feasibility of this method, showing that the ideal measure is more effective and simpler than existing methods.