Group decision making with preference information on alternatives has become a very active research field over the last decade. Especially, the investigation on the group decision making problems based on different preference formats has attracted great interests from researchers recently and some approaches have been developed for dealing with these problems. However, the existing approaches can only be suitable for handling the subjective preference information. In this paper, we investigate the multiple attribute group decision making (MAGDM) problems, in which the attribute values (objective information) are given as non-negative real numbers, the information about attribute weights is to be determined, and the decision makers have their subjective preferences on alternatives. The provided subjective preference information can be represented in three well-known exact preference formats: 1) utility values; 2) fuzzy preference relations; and 3) multiplicative preference relations. We first set up three constrained optimization models integrating the given objective information and each of three preference formats respectively, and then based on these three models, we establish an integrated constrained optimization model to derive the attribute weights. The obtained attribute weights contain both the subjective preference information given by all the decision makers and the objective information. Thus, a straightforward and practical method is provided for MAGDM with multiple types of exact preference formats.
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