随机模糊环境下的命题逻辑真度理论  

Truth Theory of Proposition Logic under Random Fuzzy Environment

作　　者：吴霞[1] 张家录[1] 

机构地区：[1]湘南学院数学与金融学院,郴州423000

出　　处：《模式识别与人工智能》2017年第4期289-301,共13页Pattern Recognition and Artificial Intelligence

基　　金：湖南省自然科学基金项目(No.2017JJ2241;16JJ6138);湖南省社会科学基金项目(No.16YBA329);湖南省教育厅科学研究重点项目(No.2014A135;13A093);湘南学院科学研究课题项目(No.2014XJ54);湖南省重点建设学科资助~~

摘　　要：在实单位区间[0,1]具有一定概率分布的基础上,引入命题逻辑公式的随机模糊意义下的真度概念,指出随机真度是已有文献中各种命题逻辑真度的共同推广.利用随机模糊真度定义公式间的随机模糊相似度,导出全体公式集上的一种伪距离——随机模糊逻辑伪距离,证明在随机模糊逻辑伪距离空间无孤立点.利用概率论中的积分收敛定理,证明一个关于随机模糊真度的极限定理.研究已有各种真度之间的联系.证明随机逻辑伪距离空间中逻辑运算的连续性,并将概率逻辑学基本定理推广至多值命题逻辑.在随机逻辑伪距离空间中提出2种不同类型的近似推理模式并应用于实际问题的近似推理.The concept of random fuzzy truth degree of logic formulas is proposed by virtue of probability distribution on real unit interval [ 0, 1 ] . It is pointed out that the random fuzzy is the common spread of truths in the valuation domain of logic formulas. Then, the concept of random fuzzy similarity degree between two logic formulas is proposed from the concept of random fuzzy truth degree. Based on it, the pseudo-metric named random fuzzy pseudo-metric is introduced on all formula sets. And it is proved that there are not isolated points in the random fuzzy logic pseudo-metric space. Moreover, by using of the integral convergence theorem in probability theory, a limit theorem of random truth degree is proved. The connection of truth degrees is illustrated by this limit theorem. Furthermore, the continuity of the logical operation in the random logic pseudo-metric space is certified and the fundamental theorems of probabilistic logic are expanded to multi-valued propositional logic. Finally, two kinds of approximate reasoning models are presented and applied to approximate reasoning of the practical problems in randomlogic pseudo-metric space.

关 键 词：命题逻辑 随机模糊真度 随机模糊相似度 逻辑伪距离空间 极限定理 近似推理 

分 类 号：O141[理学—数学]