Truth degree and falsity degree of intuitionistic fuzzy proposition are two truth values with linguistic hedge. In this paper, we constructed linguistic truth-valued intuitionistic propositional logic (LTV-IP) based on linguistic truth-valued lattice implication algebra (LIA) which can express both the comparable and incomparable truth values. Some logic properties regarding reasoning are then obtained. Especially, the implication operation of LTV-IP can be deduced from four times implication of their truth values. Finally, we discussed the satisfiable problem of LTV-IP and proposed resolution principle of LTV-IP.
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