A Novel Approach to Multi-Attribute Group Decision-Making with q -Rung Picture Linguistic Information

摘要

The proposed q -rung orthopair fuzzy set ( q -ROFS) and picture fuzzy set (PIFS) are two powerful tools for depicting fuzziness and uncertainty. This paper proposes a new tool, called q -rung picture linguistic set ( q -RPLS) to deal with vagueness and impreciseness in multi-attribute group decision-making (MAGDM). The proposed q -RPLS takes full advantages of q -ROFS and PIFS and reflects decision-makers’ quantitative and qualitative assessments. To effectively aggregate q -rung picture linguistic information, we extend the classic Heronian mean (HM) to q -RPLSs and propose a family of q -rung picture linguistic Heronian mean operators, such as the q -rung picture linguistic Heronian mean ( q -RPLHM) operator, the q -rung picture linguistic weighted Heronian mean ( q -RPLWHM) operator, the q -rung picture linguistic geometric Heronian mean ( q -RPLGHM) operator, and the q -rung picture linguistic weighted geometric Heronian mean ( q -RPLWGHM) operator. The prominent advantage of the proposed operators is that the interrelationship between q -rung picture linguistic numbers ( q -RPLNs) can be considered. Further, we put forward a novel approach to MAGDM based on the proposed operators. We also provide a numerical example to demonstrate the validity and superiorities of the proposed method.