The Theory of t Absolute Randomized Truth Degree in Goguen n-valued Propositional Logic System of Adding Two Operators

Abstract

Using the randomization method of valuation set, we firstly give the definition of t absolute randomized truth degree of propositional formula in Goguen n-valued propositional logic system of adding two operators (t takes～,Δ), and prove that some inference rules such as MP, HS,intersection inference ,union inference and some related properties of t absolute randomized truth degree; Secondly we introduce the concepts of t absolute randomized similarity degree and t absolute randomized pseudo-distance of propositional formulas, prove that some good properties of t absolute randomized similarity degree, meanwhile discuss the continuity problem of operators ～, Δ, →, ∨, ∧ with respect to t absolute randomized pseudo-distance ρ_D in t absolute randomized logical metric space (F(S,ρ_D); Then we obtain that the concepts of t absolute randomized divergence degree and t absolute randomized consistency degree of propositional formulas theory Γ and some good properties between them; Finally, we introduce that three different types of approximate reasoning patterns in t absolute randomized logical metric space, and they are proved to be equivalent.