Cauchy Single-Valued Neutrosophic Numbers and Their Applications in MAGDM

The neutrosophic sets and numbers have an important role in modeling the problems. Recently, studies on neutrosophic numbers and single-valued neutrosophic numbers which is a subclass of neutrosophic numbers have increased, rapidly. Cauchy distribution is an important concept in the statistic. In this paper, the notion of Cauchy single-valued neutrosophic numbers (CSVNNs) and α−cuts are introduced based on the Cauchy distribution formula. Summation, multiplication, and division operations between two CSVNNs are defined and given related examples. Also, the score functions of CSVNNs, arithmetic and geometric aggregation operators of them are described. Based on the defined new concepts, a multi-attribute group decision-making method is developed. Finally, to illustrate how the proposed method works, an application of the proposed method in the selection of a project to be supported and funded is developed. In this method, for each of the criteria, different score functions are determined by using the aggregation operators and score functions of the CSVNNs. Then, evaluations of the decision-makers are transformed into new values under the derived score functions for the decision. In applications, in general, decision-makers assign to criteria some values between 0 and 1 directly. In the method proposed in this paper, weights of the criteria are considered as the different functions. Therefore this method presents a more general perspective on decision-making problems.