Six-element linguistic truth-valued intuitionistic propositional logic

Truth degree and falsity degree of intuitionistic fuzzy proposition are two truth values with linguistic hedge. We consider the hedge operators using a qualitative method. Six kinds of qualitative values of the hedge variable with their qualitative operations are presented in this paper. In this paper, six-element linguistic truth-valued propositional logic based on lattice implication algebra is constructed. Some logic properties regarding reasoning are then obtained which can express both the comparable and incomparable truth values. Based on the conjunctive normal form of generalized clause, the satisfiability problem of linguistic truth-valued intuitionistic fuzzy propositional logic formula is discussed. Especially, the implication operation of linguistic truth-valued intuitionistic fuzzy propositional logic can be deduced from four times implication of their truth values. Therefore, we can use more information in the process of reasoning and eventually improve the precision of reasoning. © 2009 Binary Information Press.