Multi-criteria Group Decision Making with Picture Linguistic Numbers

Abstract

In 2013, Cuong and Kreinovich defined picture fuzzy set (PFS) as a direct extension of fuzzy set (FS) and intuitionistic fuzzy set (IFS). Motivated by PFS and fuzzy linguistic approach, this paper introduces the concept of picture linguistic number (PLN).  For multi-criteria group decision making (MCGDM) problems with picture linguistic information, we define a score index and two accuracy indexes of PLNs, and propose an approach for the comparison between two PLNs. Simultaneously, the operation laws for PLNs are defined and the related properties are studied. Further, some aggregation operations are developed: picture linguistic arithmetic averaging (PLAA), picture linguistic weighted arithmetic averaging (PLWAA), picture linguistic ordered weighted averaging (PLOWA) and picture linguistic hybrid averaging (PLHA) operators. Finally, based on the PLWAA and the PLHA operators, we propose an approach to handle MCGDM under PLNs environment.