Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making

Due to some drawbacks of the correlation coefficient between single valued neutrosophic sets (SVNSs) in dealing with decision-making problems and clustering analysis, the existing correlation coefficient may produce no defined phenomenon or its some results are not consistent with reality in some situations. In order to overcome these disadvantages, we propose an improved correlation coefficient of SVNSs and investigate its properties, and then extend it to a correlation coefficient between interval neutrosophic sets (INSs). Furthermore, we apply them to multiple attribute decision-making problems with single valued neutrosophic information and interval neutrosophic information. In the decision-making methods, through the weighted correlation coefficient between each alternative and the ideal alternative, we can obtain the ranking order of all alternatives and the best one. The proposed decision-making methods can effectively deal with decision-making problems with the incomplete, indeterminate, and inconsistent information which exist commonly in real situations. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed decision-making approaches under single valued neutrosophic and interval neutrosophic environments.