Abstract: The symmetric Kullback-Leibler (K-L) distance is adopted considering the preference ratios of decision makers (DM) for deterministic and uncertain terms of a uncertain number to directly determine the objective weights of mixed attribute decisions involving uncertain information. This approach first converts the indicators of mixed data into binary connection numbers and further divides them into two-tuple numbers. These converted numbers are normalized for comparison of various attributes. Then the symmetric K-L distances among indicators of each attribute are calculated. Moreover, the symmetric K-L distances of each attribute are summarized as the initial objective weight. It is normalized to obtain the final objective weight of each attribute. The numerical example shows that the proposed determination method of objective weights can minimize the information loss with unified processing and simple principles. Besides, it can effectively solve the problem of determining objective attribute weights containing uncertain information, which also verifies that the subjective preferences of DMs have a significant effect on the determination of objective weights.

Key words: symmetric K-L distances, subjective preferences, mixed attributes, attributes, objective weights