The consistency measures of multi-granularity linguistic group decision making

Abstract

When different experts have different uncertainty degrees on the phenomenon, several linguistic term sets with different granularity of uncertainty are necessary. In this paper, we deal with the consistency problem with multi-granularity linguistic term sets applied to group decision making. Firstly, we develop a transformation model to maintain the uncertainty degrees of different granularity associated with each expert. We use the uncertain linguistic variables as the unified form. Some computational rules about uncertain linguistic variables are given. Then consistency index of linguistic preference relations based on the distance of a multi-granularity linguistic preference relation is defined. Chi-square statistic is used to establish the consistency thresholds. Finally two numerical examples are used to show the process and effects of our new proposed method.