A Novel Method for Decision Making by Double-Quantitative Rough Sets in Hesitant Fuzzy Systems

Abstract

In some complex decision-making issues such as economy, management, and social development, decision makers are often hesitant to reach a consensus on the decision-making results due to different goals. How to reduce the influence of decision makers’ subjective arbitrariness on decision results is an inevitable task in decision analysis. Following the principle of improving the fault-tolerance capability, this paper firstly proposes the graded and the variable precision rough set approaches from a single-quantitative decision-making view in a hesitant fuzzy environment (HFEn). Moreover, in order to improve the excessive overlap caused by the high concentration of single quantization, we propose two kinds of double-quantitative decision-making methods by cross-considering relative quantitative information and absolute quantitative information. The proposal of this method not only solves the fuzzy system problem of people’s hesitation in the decision-making process, but also greatly enhances the fault-tolerant ability of the model in application. Finally, we further compare the approximation process and decision results of the single-quantitative models and the double-quantitative models, and explore some basic properties and corresponding decision rules of these models. Meanwhile, we introduce a practical example of housing purchase to expound and verify these theories, which shows that the application value of these theories is impressive.