**Some** *q***-Rung Dual Hesitant Fuzzy Heronian Mean Operators with Their Application to Multiple Attribute Group Decision-Making**

#### **Yuan Xu 1, Xiaopu Shang 1,\*, Jun Wang 1, Wen Wu 1 and Huiqun Huang 2**


Received: 21 September 2018; Accepted: 7 October 2018; Published: 10 October 2018

**Abstract:** The *q*-rung orthopair fuzzy sets (*q*-ROFSs), originated by Yager, are good tools to describe fuzziness in human cognitive processes. The basic elements of *q*-ROFSs are *q*-rung orthopair fuzzy numbers (*q*-ROFNs), which are constructed by membership and nonmembership degrees. As realistic decision-making is very complicated, decision makers (DMs) may be hesitant among several values when determining membership and nonmembership degrees. By incorporating dual hesitant fuzzy sets (DHFSs) into *q*-ROFSs, we propose a new technique to deal with uncertainty, called *q*-rung dual hesitant fuzzy sets (*q*-RDHFSs). Subsequently, we propose a family of *q*-rung dual hesitant fuzzy Heronian mean operators for *q*-RDHFSs. Further, the newly developed aggregation operators are utilized in multiple attribute group decision-making (MAGDM). We used the proposed method to solve a most suitable supplier selection problem to demonstrate its effectiveness and usefulness. The merits and advantages of the proposed method are highlighted via comparison with existing MAGDM methods. The main contribution of this paper is that a new method for MAGDM is proposed.

**Keywords:** *q*-rung orthopair fuzzy set; *q*-rung dual hesitant fuzzy; *q*-rung dual hesitant fuzzy Heronian mean; multiple attribute group decision-making
