A model for handling linguistic terms in the framework of lattice-valued logic LF(X)

In this paper, focus on uncertainties, especially the incomparability, a framework of decision making with linguistic information is presented from the viewpoint of lattice-valued first-order logic LF(X) based on lattice implication algebra. Concretely, the definitions of lattice implication algebra and proof in the lattice-valued first-order logic LF(X) are given firstly. Then the feature of each stage in a linguistic-information-based decision making process is analyzed on the ground of a typical problem. Next, taking a linguistic term as a logical formula, a model for treating linguistic information is presented and compared with other methods on an example. Example has shown that the presented approach 1) doesn't require the using of fuzzy sets for interpretation of linguistic terms; 2) doesn't require the meanings of linguistic terms having predefined totally order, and 3) doesn't require a linguistic term must take unique interpretation.