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

#### **Li Li 1, Runtong Zhang 1,\*, Jun Wang 1, Xiaopu Shang 1 and Kaiyuan Bai 2**


Received: 20 April 2018; Accepted: 14 May 2018; Published: 18 May 2018

**Abstract:** 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.

**Keywords:** *q*-rung picture linguistic set; Heronian mean; *q*-rung picture linguistic Heronian mean; multi-attribute group decision-making
