Abstract
In this paper, the multi-person decision making problems with various different types of incomplete linguistic preference relations are studied. Some new concepts, including incomplete uncertain linguistic preference relation, incomplete triangular fuzzy linguistic preference relation, incomplete trapezoid fuzzy linguistic preference relation, expected incomplete linguistic preference relation and acceptable expected incomplete linguistic preference relation, are defined. Based on some transformation functions, all these types of incomplete linguistic preference relations are transformed into the expected incomplete linguistic preference relations. By using the additive consistency property, the acceptable expected incomplete linguistic preference relations are then extended to the complete linguistic preference relations. Moreover, an approach is proposed for multi-person decision making based on multiple types of incomplete linguistic preference relations including incomplete traditional linguistic preference relations, incomplete uncertain linguistic preference relations, incomplete triangular fuzzy linguistic preference relations and incomplete trapezoid fuzzy additive linguistic preference relations.
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