For multiple attributes decision making (MADM), D numbers theory has been widely used to deal with uncertain and incomplete information. However, the incomplete information is abandoned in the D numbers' integration representation. This results in unreasonable conclusions in some real world applications. To overcome this drawback, this paper proposes an improved D numbers' integration representation method, by effectively allocating the incomplete information into decision making according to the original value of D numbers. The proposed method is applied to assess the performance of different types of motorcycles. The results show that the proposed method can effectively increase both the accuracy and efficiency of assessment when compared with the original D numbers theory.

D numbers theory is an appropriate method to deal with the information of uncertainty and incompleteness when making a reasonable decision. Previous D numbers theory provides a rule to combine multiple D numbers. However, the commutative law is not satisfied in the rule of combining multiple D numbers. In this paper, a modified method for multiple D numbers combination is proposed. The proposed method defines a new function for multiple D numbers combination which is mainly determined by the original value of D numbers. Then the proposed combination rule is applied to environmental impact assessment (EIA); our results show that the proposed method is efficient for multiple D numbers combination and it is useful when dealing with uncertainty and incompleteness.

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