| D-逻辑度量空间与近似推理 |
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| 引用本文： | 惠小静,王国俊. D-逻辑度量空间与近似推理[J]. 南京大学学报(自然科学版), 2007, 24(2): 249-257 |
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| 作者姓名： | 惠小静 王国俊 |
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| 作者单位： | 延安大学数学与计算机科学学院,陕西延安,716000;延安大学数学与计算机科学学院,陕西延安,716000;陕西师范大学数学研究所,陕西西安,710062 |
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| 摘 要： | 通过随机化赋值集的方法,在二值逻辑中提出了公式的 D- 随机真度概念,证明了全体公式的 D-随机真度之集在[0,1]中没有孤立点;提出了 D- 逻辑伪距离和 D- 逻辑度量空间,证明了该空间中没有孤立点;指出当取均匀概率测度,且各概率测度均为 1/2 时,D- 随机真度就转化为计量逻辑学中的真度,同时两公式间的 D- 逻辑伪距离就转化为计量逻辑学中的伪距离,从而建立了更具一般性的随机逻辑度量空间;最后在 D- 逻辑度量空间中提出了3种不同类型的近似推理模式,并证明了这三种模式是等价的.
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| 关 键 词： | D-随机化映射 D-随机真度 D-相似度 D-逻辑度量空间 近似推理 |
| 修稿时间： | 2007-10-08 |
D-LOGIC METRIC SPACE AND APPROXIMATE REASONING |
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| Hui Xiaojing,Wang Guojun. D-LOGIC METRIC SPACE AND APPROXIMATE REASONING[J]. Journal of Nanjing University: Nat Sci Ed, 2007, 24(2): 249-257 |
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| Authors: | Hui Xiaojing Wang Guojun |
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| Abstract: | By means of randomization,the concept of D-randomized truth degree of formulas in two-valued propositional logic is introduced.It is proved that the set of values of D-randomized truth degree of formulas has no isolated point in[0,1];The concepts of D-logic pseudo-metric and D-logic metric space are also introduced.It is proved that there is no isolated point in the space;The new built D-randomized concepts axe extensions of the corresponding concepts in quantified logic;Moreover, three different types of approximate reasoning patterns are proposed in D-logic metric space and it is proved that they are equivalent to each other. |
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| Keywords: | D-randomized mapping D-randomized truth degree D-similarity D-logic metric space approximate reasoning |
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