*Article* **Hesitant Fuzzy Linguistic Aggregation Operators Based on the Hamacher t-norm and t-conorm**

**Jianghong Zhu 1,\* and Yanlai Li 1,2**


Received: 11 May 2018; Accepted: 30 May 2018; Published: 31 May 2018

**Abstract:** Hesitant fuzzy linguistic (HFL) term set, as a very flexible tool to represent the judgments of decision makers, has attracted the attention of many researchers. In recent years, some HFL aggregation operators have been developed to aggregate the HFL information. However, most of these operators are proposed based on the Algebraic product and Algebraic sum. In this paper, we presented some HFL aggregation operators to handle HFL information based on Hamacher triangle norms. We first define new operational laws on the HFL element according to Hamacher triangle norms. Then we present a family of HFL Hamacher aggregation operators, including the HFL Hamacher weighted averaging, HFL Hamacher weighted geometric, HFL Hamacher power weighted averaging and HFL Hamacher power weighted geometric operators and their generalized forms. We also investigate some special cases and properties of these operators in detail. Furthermore, we develop two approaches based on the proposed operators to deal with the multi-criteria decision-making problem with HFL information. Finally, a numerical example with regard to choosing a suitable city to release sharing car is provided to illustrate the feasibility of the proposed method, and the advantages of the proposed methods are shown by conducting a sensitivity and comparative analysis.

**Keywords:** hesitant fuzzy linguistic term set; Hamacher t-norm and t-conorm; power aggregation operator; multi-criteria decision-making
