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.