A three-way decision based multi-attribute decision-making with intuitionistic fuzzy β-covering

Multi-attribute decision making (MADM) is an important part of modern decision science, and its theories and methods are widely used in many fields, such as engineering design, economics, management and military. The essence of MADM is to use the existing decision-making information to rank or select a set of (limited) alternatives in a certain way. Using three-way decision (3WD) to solve the MADM problem has become a hot topic today. In classical 3WD models, the equivalence relation of many decision-making methods is too strict, so we have to face a certain decision risk when using classical 3WD to solve real-life problems. In view of this, we aim to put forward a novel 3WD model on the basis of intuitionistic fuzzy /3-covering (IF/3C) in MADM problems. Firstly, we propose a novel ideal positive degree for ranking intuitionistic fuzzy numbers (IFNs). Secondly, we establish a method of conditional probability calculation formula based on the novel ideal positive degree, and obtain the loss functions as per the aggregated operator and the novel ideal positive degree of IFNs. Then a novel 3WD method based on IF/3C is proposed. Finally, we apply the proposed method to solve the teacher training professional certification problem. By comparison and experimental analysis with existing methods, the results show that the proposed method is effective and credible to deal with MADM problems.& COPY; 2023 Elsevier B.V. All rights reserved.