A Three-Way Acceleration Approach for Interval-Valued Multi-Attribute Decision-Making Problems

As an essential part of modern intelligent decision-making science, multi-attribute decision-making problems can effectively select and rank all candidate schemes under multiple indicators. Because of the complexity of the real environment and the uncertainty of the decision-making problem, interval numbers are often used to represent the evaluation information of the object. The existing methods of the multi-attribute decision-making problems rarely use the object set but give the decision results by selection or ranking, which often have strong subjectivity. We propose a ranking method from an acceleration viewpoint based on the three-way decision model to solve the interval-valued multi-attribute decision-making problem. A distance measure of two objects is a measure that describes the relationship between objects. Therefore, the fuzzy dominance distance is introduced to express order relations among objects. First, we present a method to compare any two interval numbers, which converts interval numbers into connection numbers according to the characteristics of interval numbers in multi-attribute decision-making problems. Second, the three-way decision theory is introduced to divide the object set into high, medium, and low dominance regions for the speed and rationality of decision-making. Finally, the multi-attribute decision-making problems can be simplified into the problem of selection in three regions by ranking the objects of the selected region. Unlike traditional methods, the experiments demonstrate that our proposed method has the lowest cost. Our method is shown to be efficient and can obtain comparable results.