Operations and aggregation method of neutrosophic cubic numbers for multiple attribute decision-making

Abstract

A neutrosophic cubic set (NCS) consists of both an interval neutrosophic set and a single-valued neutrosophic set. Hence, NCSs are very suitable for expressing the hybrid information of both the interval neutrosophic set (related to the uncertain part of the information) and the single-valued neutrosophic set (related to the certain part) simultaneously. However, there is little research on operations and applications of NCNs in existing literature. First, therefore, this paper proposes the operations of neutrosophic cubic numbers (NCNs), which are basic elements in NCSs. Second, we define the score, accuracy, and certainty functions, along with a ranking method for NCNs. Third, we develop a neutrosophic cubic number weighted arithmetic averaging (NCNWAA) operator and a neutrosophic cubic number weighted geometric averaging (NCNWGA) operator in order to aggregate NCN information and indicate their properties. Then, a multiple attribute decision-making method based on the NCNWAA or NCNWGA operator and the ranking method of NCNs is established under a NCN environment. Finally, an illustrative example about the selection problem of investment alternatives is provided in order to demonstrate the application and feasibility of the developed approach.