This paper presents operational laws along with their cosine measure for the numbers whose base is an interval value and study their properties. Consequent upon these definitions and properties neutrosophic cubic weighted exponential averaging and dual neutrosophic cubic weighted exponential averaging aggregation operators are defined. A multi attribute decision making method is then developed for proposed aggregation operators. An example is constructed as an application. The validity of multi attribute decision making method is also tested and comparative analysis is provided to compare these aggregation operators with existing results.