Simplified neutrosophic harmonic averaging projection-based method for multiple attribute decision-making problems

A simplified neutrosophic set is a subclass of a neutrosophic set and includes the concepts of a single valued neutrosophic set and an interval neutrosophic set, which can be used in real science and engineering applications with the incomplete, indeterminate and inconsistent information which exists commonly in real situations. Then, projection measure is a very suitable tool for dealing with multiple attribute decision-making problems because it can consider not only the distance but also the included angle between objects evaluated. Therefore, the main purpose of the paper is to present a simplified neutrosophic harmonic averaging projection measure and its multiple attribute decision making method with simplified neutrosophic information. Through the harmonic averaging projection measure between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily obtained as well. Finally, an illustrative example demonstrates the application and effectiveness of the proposed projection measure method in a simplified neutrosophic multiple attribute decision-making environment.