A numerical two-scale model of multi-granularity linguistic variables and it´s application to group decision making

Many group decision making (GDM) problems under uncertain environments have vague and imprecise information in linguistic variable formats. Multi-granularity linguistic method with the process of symbolic computation is a typical tool to solve such problems, and can be associated with the popular computing with words domain. In the paper, we present numerical two-scale model which is the extension of symbolic computation model. Firstly, numerical two-scale representation model is proposed with two scale measurements. One is used to reflect the order of linguistic variable and the other is used to model vagueness. Secondly, we give numerical two-scale computational model in group decision making. We discuss the rules of symbolic method which directly compute with the two numerical measurements. Finally, some aggregation operators are developed. The new model has the advantage of avoiding the vague information losing without adding the calculation difficulty.