Rough Neutrosophic Multi-Attribute Decision-Making Based on Grey Relational Analysis

This paper presents rough netrosophic multiattribute decision making based on grey relational analysis. While the concept of neutrosophic sets is a powerful logic to deal with indeterminate and inconsistent data, the theory of rough neutrosophic sets is also a powerful mathematical tool to deal with incompleteness. The rating of all alternatives is expressed with the upper and lower approximation operator and the pair of neutrosophic sets which are characterized by truth-membership degree, indeterminacy-membership degree, and falsitymembership degree. Weight of each attribute is partially known to decision maker. We extend the neutrosophic grey relational analysis method to rough neutrosophic grey relational analysis method and apply it to multiattribute decision making problem. Information entropy method is used to obtain the partially known attribute weights. Accumulated geometric operator is defined to transform rough neutrosophic number (neutrosophic pair) to single valued neutrosophic number. Neutrosophic grey relational coefficient is determined by using Hamming distance between each alternative to ideal rough neutrosophic estimates reliability solution and the ideal rough neutrosophic estimates un-reliability solution. Then rough neutrosophic relational degree is defined to determine the ranking order of all alternatives. Finally, a numerical example is provided to illustrate the applicability and efficiency of the proposed approach.