− In this paper, we present some definitions of neutrosophic refined sets such as; union,intersection, convex and strongly convex in a new way to handle the indeterminate information andinconsistent information. Also we have examined some desired properties of neutrosophic refinedsets based on these definitions. Then, we give distance measures of neutrosophic refined sets withproperties. Finally, an application of neutrosophic refined set is given in medical diagnosis problem(heart disease diagnosis problem) to illustrate the advantage of the proposed approach