A 2-tuple fuzzy linguistic representation model for computing with words

The fuzzy linguistic approach has been applied successfully to many problems. However, there is a limitation of this approach imposed by its information representation model and the computation methods used when fusion processes are performed on linguistic values. This limitation is the loss of information caused by the need to express the results in the initial expression domain that is discrete via an approximate process. This loss of information implies a lack of precision in the final results from the fusion of linguistic information. In this paper, we present tools for overcoming this limitation. The linguistic information will be expressed by means of 2-tuples, which are composed by a linguistic term and a numeric value assessed in [ 0.5, 0.5). This model allows a continuous representation of the linguistic information on its domain, therefore, it can represent any counting of information obtained in a aggregation process. Together with the 2-tuple representation model we shall develop a computational technique for computing with words (CW) without any loss of information. Finally, different classical aggregation operators will be extended to deal with the 2-tuple linguistic model.