A Method for Dealing with Multi-granularity and Multi-scale Linguistic Information based on Modified Proportional 2-tuple

Abstract

Multi-granularity linguistic information has been studied by researchers in many disciplines, in which the scale of linguistic term sets is usually restricted in domain [0, 1]. In this paper, we consider the multiple attribute group decision making (MAGDM) problems, in which the evaluation of each alternative with respect to each attribute is provided by several experts of the corresponding field. In order to convey the preferences of different experts exactly and to describe the characteristics of different attributes, linguistic term sets with different granularities and different scales have been proposed to express their evaluation values. Moreover, the performance values given by the experts take the form of modified proportional 2-tuples. In this process, the modified proportional 2-tuple, its comparative rules as well as several aggregation operators have been proposed. A new method has been proposed to achieve a basic modified linguistic term set (BMLTS) and a transformation function has been defined to make the performance values uniform. An example is given to illustrate the applicability and flexibility of the method.