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The interval multiple attribute decision-making problems are studied in this paper, where the preference information on attributes is expressed with preference orderings, linguistic terms, interval numbers, and inequality constraints among partial attribute weights. An approach is proposed to determine the attribute weights based on the preference information on attributes and the interval decision matrix. Firstly, preference orderings, linguistic terms, and interval numbers are normalized and aggregated into the group opinions, based on which an optimization model is set up to calculate the subjective attribute weights by including inequality constraints among partial attribute weights in the model. Then, based on the interval decision matrix, the entropy method is adopted to calculate the objective attribute weights, which is integrated with the subjective weights so that both the subjective preference information and the objective information in the decision matrix are reflected. Finally, an example is used to illustrate the proposed approach.

An Approach to Determining Attribute Weights Based on Integrating Preference Information on Attributes with Decision Matrix