Entropy Based Grey Relational Analysis Method for Multi- Attribute Decision Making under Single Valued Neutrosophic Assessments

TLDR: In this paper, the grey relational analysis method is applied to multi-attribute decision making problem with single-valued neutrosophic attribute values, where the rating of all alternatives is expressed with a singlevalued set, which is characterised by truth-membership degree, indeterminacy-memberships degree, and falsity-Membership degree.

Abstract: In this paper we investigate multi-attribute decision making problem with single-valued neutrosophic attribute values. Crisp values are inadequate to model real life situation due to imprecise information frequently used in decision making process. Neutrosophic set is one such tool that can handle these situations. The rating of all alternatives is expressed with single-valued neutrosophic set which is characterised by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree. Weight of each attribute is completely unknown to decision maker. We extend the grey relational analysis method to neutrosophic environment and apply it to multi-attribute decision making problem. Information entropy method is used to determine the unknown attribute weights. Neutrosophic grey relational coefficient is determined by using Hamming distance between each alternative to ideal neutrosophic estimates reliability solution and the ideal neutrosophic estimates un-reliability solution. Then neutrosophic relational degree is defined to determine the ranking order of all alternatives. Finally, an example is provided to illustrate the application of the proposed method.