计量逻辑学中的反射变换  

Reflexive Transformation in Quantitative Logic

作　　者：王庆平[1,2] WANG Qing-ping(School of Statistics,Jiangxi University of Finance & Economics,Nanchang 330013,China;Research Center of Applied Statistics,Jiangxi University of Finance & Economics,Nanchang 330013,China)

机构地区：[1]江西财经大学统计学院,江西南昌330013 [2]江西财经大学应用统计研究中心,江西南昌330013

出　　处：《模糊系统与数学》2018年第6期33-40,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61562030)

摘　　要：首先在连续值L*逻辑度量空间中,给出了公式集F(S)上的反射变换φ:F(S)→F(S)的概念,证明了该反射变换φ是F(S)上的自同构映射。其次证明了计量逻辑学中公式的真度,公式间的相似度与伪距离在反射变换下保持不变,而且证明了在反射变换下三种近似推理是等价的。最后,研究了反射变换φ的不动点的性质。In this paper, a reflexive transformation φ:F(S)→F(S) on F(S) in the logic system L* is proposed, which is an automorphism of F(S). In Quantitative Logic, it is proved that the concepts of truth degree, similarity degree and pseudo-distance are remain under the reflexive transformation φ. Moreover, three different approximate reasoning patterns are equivalent in the system L*. Finally, the properties of fixed points under the reflexive transformation φ are researched.

关 键 词：计量逻辑学 反射变换 真度 近似推理 不动点 

分 类 号：O159[理学—数学]