Linguistic Truth-Valued Lattice Implication Algebra and Its Properties

The subject of this work is to establish a mathematical framework that provides the basis and tool for automated reasoning and uncertainty reasoning based on linguistic information. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic terms, specially, the symbolic approach acts by direct computation on linguistic terms. An algebra model with linguistic terms, which is based on a logical algebraic structure, i.e., lattice implication algebra, is constructed and applied to represent imprecise information and deal with both comparable and incomparable linguistic terms (i.e., non-ordered linguistic terms). Some properties and its substructures of this algebraic model are discussed