Decision-Making Method Based on Grey Relation Analysis and Trapezoidal Fuzzy Neutrosophic Numbers Under Double Incomplete Information and its Application in Typhoon Disaster Assessment

Multi-attribute decision-making problems under the trapezoidal fuzzy neutrosophic numbers environment are complex, particularly when the attribute value data are incomplete, and the attribute weight is completely unknown. As a solution, this study proposes a decision-making method based on information entropy and grey theory. First, regarding the problem of attribute value incompleteness in the decision matrix, a method of defining the missing information using trapezoidal fuzzy neutrosophic numbers is proposed, which is simpler and more reasonable than the traditional method of complements. Regarding the problem of completely unknown attribute weights, the definition of new trapezoidal fuzzy neutrosophic entropy is proposed and used to determine the attribute weight. Thereafter, the grey relation analysis method of grey theory is used to rank alternatives and select the best one. Finally, an illustrative example about typhoon disaster assessment is presented to show the feasibility and effectiveness of the proposed method. Finally, the advantages of the proposed method are illustrated by comparison with other methods from multiple aspects.