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

Abstract

Abstract. The purpose of this paper is to introduce multiattribute decision making based on the concept of interval neutrosophic sets. While the concept of neutrosophic sets is a powerful tool to deal with indeterminate and inconsistent data, the interval neutrosophic set is also a powerful mathematical tool as well as more flexible to deal with incompleteness. The rating of all alternatives is expressed in terms of interval neutrosophic values characterized by interval truth-membership degree, interval indeterminacy-membership degree, and interval falsity-membership degree. Weight of each attribute is partially known to the decision maker. The authors have extended the single valued neutrosophic grey relational analysis method to interval neutrosophic environment and applied it to multiattribute decision making problem. Information entropy method is used to obtain the unknown attribute weights. Accumulated arithmetic operator is defined to transform interval neutrosophic set into single value neutrosophic set. Neutrosophic grey relational coefficient is determined by using Hamming distance between each alternative to ideal interval neutrosophic estimates reliability solution and the ideal interval neutrosophic estimates unreliability solution. Then interval neutrosophic relational degree is defined to determine the ranking order of all alternatives. Finally, an example is provided to illustrate the applicability and effectiveness of the proposed approach.