Studies On Lattice-valued Propositional Logic And Its Resolution-based Automatic Reasoning Based On Linguistic Truth-valued Lattice Implication Algebra

Uncertain information processing exist in the processing of decision making,risk analysis, evaluation and so on. Based on lattice implication algebra and fuzzy or incomparable linguistic values, we construct linguistic truth-valued logic system to process comparable or incompara-ble linguistic information. Moreover, we study theory and method of linguistic truth-valued resolution based on lattice implication algebra. We also study the theory and reasoning method of linguistic truth-valued intuitionistic fuzzy logic. The main results are as follows:1. Method of linguistic-valued information processing(1)Hedge algebra and 2-tuple linguistic representation model are analyaed in the paper.(2)The structure and reasoning properties of 18-element and 2n-element linguistic truth-valued lattice implication algebra are discussed.2. Lattice propositional logic system based on linguistic truth-valued lattice implication algebra(1)Some special properties and resolution-based reasoning on the filter of 6-elements linguistic truth-valued propositional logic system hold.(2)The reasoning properties of linguistic truth-valued propositional logic system based on 2n-element lattice implication algebra are obtained.(3)Satisfiable problem of linguistic truth-valued propositional logic system are solved. Linguistic truth-valued resolution-based automated reasoning method on the filter are given.3. Linguistic truth-valued intuitionistic fuzzy algebra(1) Based on 18-element linguistic truth-valued lattice implication algebra, linguistic truth-valued intuitionistic fuzzy algebra LI18 is established, moreover, LI18 is generalized to In linguistic truth-valued intuitionistic fuzzy lattice LI2n=(LI2n,∪,∩,→, ((hn,t), (hn,f))), ((h1,t), (h1,f)) based on 2n linguistic truth-valued lattice implication algebra.(2) Algebra properties of linguistic truth-valued intuitionistic fuzzy lattic LI2n are ob-tained and the implication operator on∨-unreduction element of LI2n are discussed. Moreover the implication properties of LI2n are obtained.(3) The linguistic truth-valued intuitionistic fuzzy lattice algebra LI2n is compared with residual lattice, MTL-algebra, BL-algebra, MV-algebra, lattice implication algebra and R0-algebra.(4) The triangle algebra structure of LI2n is given. 4. Linguistic truth-valued intuitionistic fuzzy propositional logic system(1) Linguistic truth-valued intuitionistic fuzzy propositional logic system LP(S) is intro-duced, and the proof and theorem of LP(S) are given.(2) The semantic of LP(S) are analyzed. The reliability and completeness of LP(S) are proved.(3) The satisfiability of formula in LP(S) is solved and the (α,β)-resolution method of LP(S) is discussed.(4) The automated reasoning of 45-element linguistic truth-valued intuitionistic fuzzy propositional logic system is given.