Incomplete linguistic preference relations and their fusion

Various linguistic preference relations, including incomplete linguistic preference relation, consistent incomplete linguistic preference relation and acceptable incomplete linguistic preference relation, are introduced. Some desirable properties of the incomplete linguistic preference relation are studied. Based on the operational laws of the linguistic evaluation scale, and the acceptable incomplete linguistic preference relation with the least judgments, we develop a simple and practical method for constructing a consistent complete linguistic preference relation by using the additive transitivity property. The method not only relieves the decision maker of time pressure and makes sufficiently using of the provided preference information, but also maintains the decision maker’s consistency level and avoids checking the consistency of linguistic preference relation. Furthermore, an approach to multi-person decision making based on incomplete linguistic preference relations is developed. The approach fuses all the consistent complete linguistic preference relations, constructed by using the individual acceptable incomplete linguistic preference relations with the least judgments, into a collective complete linguistic preference relation, and then the overall information corresponding to each decision alternative is aggregated. Finally, an illustrative example is given.