随机模糊环境下的命题逻辑真度理论

发布时间：2018-02-26 05:05

本文关键词： 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　出处：《模式识别与人工智能》2017年04期 　论文类型：期刊论文

【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.
[Abstract]:On the basis of the probability distribution of real unit interval [0 ~ 1], the concept of truth degree in the sense of random ambiguity of propositional logic formula is introduced. It is pointed out that random truth degree is a common generalization of various propositional logic truth degrees in existing literatures. By using random fuzzy truth degree to define random fuzzy similarity between formulas, a pseudo-distance of random fuzzy logic pseudo-distance on the set of all formulas is derived. It is proved that there are no isolated points in random fuzzy logic pseudo distance space. A limit theorem about random fuzzy truth degree is proved. The relation between various true degrees is studied. The continuity of logic operation in random logic pseudo distance space is proved. The basic theorem of probabilistic logic is extended to the most valued propositional logic and two different types of approximate reasoning models are proposed in the pseudo-distance space of stochastic logic and applied to the approximate reasoning of practical problems.
【作者单位】：湘南学院数学与金融学院;
【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~~
【分类号】：O141

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