The Study Of Uncertainty Reasoning For Linguistic Truth-Valued Lattice-Valued First-Order Logic

The idea of linguistic truth-valued lattice implication algebra is introduced into the lattice-valued first-order logic in this thesis, the study presented in this dissertation concentrates on some structures of linguistic truth-valued lattice implication algebra, theories and methods of uncertainty reasoning based on linguistic truth-valued lattice-valued first-order logic Lv(n×2)F(X) and linguistic truth-valued gradational lattice-valued first-order logic Lv(n×2)fl·The innovation and main results are summarized as follows:Part One. The study of lattice implication algebra1. According to the lattice implication polynomial, the notion of inequality in lattice implication algebra was redefined. The several characterizations of solution set in unary lattice implication algebra inequalities are investigated, and the constructions of filters and ideals by some solution sets are obtained.2. The concept of weak Li-ideals is defined, weak Li-ideals and topological space properties based on weak Li-ideals of lattice implication algebra are investigated, and obtained the necessary and sufficient condition of second countable axiom in (L,TW(L)).3. The notion of normed lattice H implication algebras, implication distance d→v—distance and∧-distance are introduced. The properties of normed implication epimorphism, normed lattice H implication homomorphism. normed lattice H implication isomorphism and normed isomorphism are given. The boundedness of convergence sequence and sequences operations (i.e.,(?),(?),∨,∧,→) to implication distance are proved.Part Two. The study on linguistic truth-valued lattice implication algebra1. The properties of linguistic truth-valued lattice implication algebra are given, and obtained(aj,bn)→(aj,bm)= (aP,bh)→(ai,,bm)(?)aj= aP and bn= bh(?) (ai,bm)→(aj,bn) = (ai,bm)→(aP,bh).2. The reasoning properties of dual molecule in linguistic truth-valued lattice implication algebra are investigated, and it is proved that operators∨,∧,→have some degree closed.3. The concept of implicative irreducible element in linguistic truth-valued lattice implication algebra is introduced, and its reasoning properties are obtained.Part Three. The study of uncertainty reasoning based on linguistic truth-valued lattice-valued first-order logic Lv(n×2)F(X)1. The uncertainty reasoning theory and approach based upon linguistic truth-valued lattice-valued first-order logic Lv(n×2)F(X) are proposed.2. The inference rules with generalized quantifiers based upon linguistic truth-valued lattice-valued first-order logic Lv(n×2)F(X) are given, and the reasonableness of these inference rules are proved.3. The uncertainty reasoning theories and approaches under two inference models based upon linguistic truth-valued lattice-valued first-order logic Lv(n×2)F(X) are proposed.Part Four. The study of uncertainty reasoning based on linguistic truth-valued gradational lattice-valued first-order logic Lv(n×2)fl1. The uncertainty reasoning theory and approach of the inference rules under the level (α0,β0)≤∧(θ∨θ')(θ≠(an,t)) based upon linguistic truth-valued gradational lattice-valued first-order logic system Lv(n×2)fl is proposed, and the reasonableness of these methods are proved.2. The regular conditons of uncertainty inference model, the uncertainty reasoning theory and approach under the set of implicative irreducible elements based upon linguistic truth-valued gradational lattice-valued first-order logic system Lv(n×2)fl are discussed.