连续值Lukasiewicz系统中命题的随机真度的研究

Research on the Propositional Randomized Truth Degree in Continuous Value Lukasiewicz Logic System

在连续值Lukasiewicz系统L∞中,建立了随机真度的概念,给出了随机真度的推理规则,基于此真度给出了命题之间的随机相似度与伪距离,并建立了随机逻辑度量空间(F(S),d),证明了常见的几种运算在该度量空间中关于伪距离是连续的,为在该逻辑系统中建立近似推理理论奠定了基础。

The concept of randomized truth degree of proposition is proposed in the continuous value fuzzy logic system L~, some inference rules of the randomized truth degree are given. Based on this randomized truth degree, the concepts of the randomized similarity and the randomized pseudo-distances are defined. At the same time, the randomized metric space is built. At last the continuity of some common operators are proved in this metric space. Therefore it lay a foundation for establishing approximate reasoning theory in this logic system.