Variable precision diversified attribute multigranulation fuzzy rough set-based multi-attribute group decision making problems

For a considered multiple attribute group decision making (MAGDM) problem, there may be different evaluation attribute set used by different decision-makers for the same decision making problem. This article investigates the diversified attribute group decision making problem by using the diversified attribute multigranulation fuzzy rough set. Firstly, we give a general description and the definition of diversified attribute fuzzy decision making information system. We then construct the 3 neighborhood according to the different attribute set over diversified attribute fuzzy decision making space. With the 6 neighborhood relation classes, we establish the diversified attribute multigranulation decision making space and investigate the rough approximation of a crisp/ fuzzy decision making object with respect to the diversified attribute multigranulation decision making space, i.e., the variable precision diversified attribute multigranulation fuzzy rough set model over diversified attribute fuzzy decision making space. Subsequently, we present some mainly conclusions and related mathematics properties for the established model. Furthermore, we explore the interrelationship between the proposed variable precision diversified attribute multigranulation fuzzy rough set model and the traditional models. Moreover, we propose a new approach to multiple attribute group decision making (MAGDM) problems with different evaluation attribute set based on variable precision diversified attribute multigranulation fuzzy rough set and VIKOR method. The background of the decision making problem, the principle and the methodology of the presented method are established as well as a particularly comparison of the existing approaches to multiple attribute group decision making with different evaluation attribute set shows the superiorities and deficiencies. At last, an numerical example of the performance appraisal for emergency preparedness of emergency management decision making is verified to illustrate the principle and procedures for this approach.