连续值Luk系统中公式的Γ-真度及其性质

Theory of Γ-truth degree of formulas in continuous-valued Lukasiewicz systemand its properties

对Lukasiewicz系统中的真度理论进行了进一步的研究。将n值Lukasiewicz系统中公式相对于有限理论的ΣΓ-真度理论与连续值Lukasiewicz系统中公式的积分真度相结合,在连续值Lukasiewicz系统中引入了公式相对于有限理论的Γ-真度理论,讨论了其中的主要性质;在公式集F(S)上引入了任意两公式相对于有限理论的Γ-伪距离,从而拓宽了真度理论的应用范围。

The truth degree theory of Lukasiewicz system is further studied.Having combined the theory of ΣΓ -truth degree of formulas in n-valued Lukasiewicz system with the integrated truth degree theory in continuous-valued Lukasiewicz system,the concept of Γ-truth degree of formulas is introduced which is relative to the finite theory in continuous-valued Lukasiewicz system,and some essential properties are discussed.Simultaneously,the Γ-pseudo-metric on F（S） is established in Lukasiewicz system by employing the theory of Γ-truth degree.These results can broaden the scope of application of truth degree theory.