Linguistic Distribution and Priority-Based Approximation to Linguistic Preference Relations With Flexible Linguistic Expressions in Decision Making

In this article, we propose the concept of flexible linguistic preference relations (FLPRs), in which the flexible linguistic expressions, a more flexible way to form linguistic expressions, are employed. Further, we present a method to rank alternatives based on preference information in FLPRs by exploring the linguistic distribution (LD) and priority-based approximation (PA) of FLPRs. In the LD-based approximation, we first present a two-stage optimization process to approximate FLPRs to distribution linguistic preference relations (DLPRs) following the principles of minimum preference loss and maximum consistency. Then in the PA process, we derive priority vectors from the DLPRs with some desired properties. Finally, a comparative analysis of the priority vectors derived from different kinds of linguistic preference relations is presented to illustrate our proposal.