A New Methodology for Neutrosophic Multi-Attribute Decision-Making with Unknown Weight Information

In this paper, we present multi-attribute decision-making problem with neutrosophic assessment. We assume that the information about attribute weights is incompletely known or completely unknown. The ratings of alternatives with respect to each attributes are considered as single-valued neutrosophic set to catch up imprecise or vague information. Neutrosophic set is characterized by three independent degrees namely truthmembership degree (T), indeterminacy-membership degree (I), and falsity-membership degree (F). The modified grey relational analysis method is proposed to find out the best alternative for multi-attribute decisionmaking problem under neutrosophic environment. We establish a deviation based optimization model based on the ideal alternative to determine attribute weight in which the information about attribute weights is incompletely known. Again, we solve an optimization model with the help of Lagrange functions to find out the completely unknown attributes weight. By using these attributes weight we calculate the grey relational coefficient of each alternative from ideal alternative for ranking the alternatives. Finally, an illustrative example is provided in order to demonstrate its applicability and effectiveness of the proposed approach.