Multi-attribute group decision making method based on neutrosophic trapezoidal fuzzy linguistic frank aggregation operators.

As we all know, there are many methods to describe the different kinds of quantitative or qualitative information. However, it is necessary to extend them to express complex information by combining the qualitative and quantitative mode. In this paper, we firstly define the neutrosophic trapezoidal fuzzy linguistic numbers (NTFLNs) by combining the neutrosophic sets (NSs) with linguistic variables (LVs) to express complex information. In addition, the Frank operations are a generalization of some existing operations with a parameter. Therefore, we extend the Frank operations to the NTFLNs, and then we propose the neutrosophic trapezoidal fuzzy linguistic Frank weighted averaging (NTFLFWA) operator and the neutrosophic trapezoidal fuzzy linguistic Frank weighted geometric (NTFLFWG) operator. Further, some desirable properties of them are studied such as idempotency, boundedness and monotonicity. Moreover, two methods based on the NTFLFWA and NTFLFWG operators for the multiple attribute group decision making (MAGDM) problems are developed. Finally, an empirical example on choice of the emergency logistics supplier is given to demonstrate the effectiveness of the developed methods.