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

TLDR

The fuzzy linguistic approach has been successfully applied to many problems, yet its fusion processes suffer from information loss due to limited representation models and computation methods, reducing precision. This paper introduces tools to eliminate that information loss. By encoding linguistic information as 2‑tuples—a linguistic term paired with a numeric value in (−0.5, 0.5)—the authors provide a continuous representation that supports loss‑free computation with words and extend classical aggregation operators to this model.

Abstract

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; 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 is expressed by means of 2-tuples, which are composed of 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. We then develop a computational technique for computing with words without any loss of information. Finally, different classical aggregation operators are extended to deal with the 2-tuple linguistic model.