The subject of this work is to establish a mathematical framework that provides the basis and tool for synthesis and evaluation analysis in decision making, especially from the logic point of view. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic assessment in decision making, specially, the symbolic approach acts by direct computation on linguistic values. A lattice-valued linguistic algebra model, which is based on a logical algebraic structure, i.e., lattice implication algebra, is applied to represent imprecise information and deal with both comparable and incomparable linguistic values (i.e., non-ordered linguistic values). Within this framework, some known weighted aggregation functions are analyzed and extended to deal with these kinds of lattice-value linguistic information.