A new D numbers’ integration rule based on pessimistic criterion

Abstract

For D numbers theory, there are some drawbacks in the D numbers’ integration rule. For example, the missing information is ignored in the final decision judgment for multi-attribute decision (MADM). For this problem, some researchers have improved the D numbers’ integration rules based on optimistic criterion for overcoming the shortcoming of D numbers’ integration rule. However, optimistic and pessimistic criterion are two sides of the coin for fuzzy environment. Therefore, in this article, a new D numbers’ integration rules based on pessimistic criterion is proposed. We improve the D numbers’ integration rules to redefine the missing information distribution rules based on pessimistic criterion. The missing information is distributed in inverse proportion to each D number according to the size of the original evidence credibility. Two examples of MADM is applied by the proposed method, the results show that the proposed method can be applied to MADM.