Normal neutrosophic frank aggregation operators and their application in multi-attribute group decision making

Normal neutrosophic set (NNS) can conveniently express random and fuzzy information, and Frank operators have the properties of generalization and flexibility. In this paper, we will extend Frank operators to Normal neutrosophic numbers (NNNs), and propose some Frank aggregation Operators for NNNs, then develop two new decision methods with NNNs. Firstly, based on Frank operators, the operational laws of NNNs are redefined, and their operational properties are proved, then the normal neutrosophic Frank averaging operator (NNFWA) and normal neutrosophic Frank weighted geometric operator (NNFWG) are developed. Further, some desirable characteristics, such as idempotency, boundedness and commutativity, are discussed in detail, and some special cases are studied. Furthermore, to deal with the multiple attribute group decision making (MAGDM) problems in which attribute values take the form of NNNs, two methods on the basis of NNFWA and NNFWG operators are developed, and they are more general and more flexible by Frank operations. Finally, an example is given to illustrate the proposed methods and demonstrate their practicality and availability.