Abstract：It is shown that a judgment of property (proposition) based on the conversion of a quantity of a attribute a(o) x into a property p(x,o) of a(o), whose judging result or the truth value of property varies according to its qualitative criterion [α,β], can be extracted as a dynamic Qualitative Mapping τp(x,[α,β]) whose parameter is criterion [α,β]. Several QM definitions are respectively given whose qualitative criteria are a interval, a vector of intervals and a grid of ndimension parallelepiped. The geometric mean that a weight w acting on the qualitative criterion [α,β], the relation between a qualitative mapping and an artificial neuron, the mechanism and the condition that a qualitative mapping for judging truth value of property converted into a pattern recognition mapping are respectively discussed. Furthermore, the degree function that a quantity of an attribute converted into a quality or a property and a mechanism fuzzized the boundary of qualitative criterion are presented too. And it’s shown that if qualitative mapping is substituted by a fuzzized conversion degree function respectively the judgment and recognition would be fuzzy. And a series of examples to test the validity of qualitative mapping and conversion degree function are given.
[1] Logical Group, Department of Philosophy, Chinese People’s University. Logic. Beijing, China: Press of Chinese People’s University, 1996, 47 (in Chinese) (中国人民大学哲学系逻辑教研室.逻辑学.北京:中国人民大学出版社, 1996, 47) [2] Tian Y. Dictionary of Thinking. Hangzhou, China: Zhejiang Education Publishing House, 1996, 280 (in Chinese) (田运. 思维辞典.杭州:浙江教育出版社, 1996, 280) [3] Jin Y L. Formal Logic. Beijing, China: People’s Press, 1979, 15 (in Chinese) (金岳霖. 形式逻辑. 北京: 人民出版社, 1979, 15) [4] Su T F. Proposition and Judgment. In: Encyclopaedia of China. Beijing, China: Encyclopaedia of China Publishing House, 1987, 625 (in Chinese) (苏天辅.命题与判断.见:中国大百科全书. 北京,中国大百科全书出版社, 1987, 625) [5] Yao B M. Quality and Quantity. In: Encyclopaedia of China. Beijing, China: Encyclopaedia of China Publishing House, 1987, 1181 (in Chinese) (姚伯茂.质与量.见:中国大百科全书.北京,中国大百科全书出版社, 1987, 1181) [6] Feng J L, Dong Z Q. A Kind of Mathematic Model of Sensation Neuron Detection Based on Attribute Abstraction and Integration. Journal of Computer Research and Development, 1997, 34(7): 487-491 (in Chinese) (冯嘉礼,董占球.基于属性整合的知觉模式生成与识别模型.计算机研究与发展, 1997, 34(7): 487-491) [7] Dong Z Q, Feng J L. A Mathematical Description of Memory Schema(I)-The Attribute Coordinate Representation of Memory Schema. Journal of Computer Research and Development, 1998, 35(8): 694-698 (in Chinese) (董占球,冯嘉礼.按模式记忆理论的数学描述(I)——记忆模式的属性坐标表示法.计算机研究与发展, 1998, 35(8): 694-698) [8] Feng J L, Zhan M. A Qualitative Mapping Model of Extract of Perception Data-Feature. Journal of Tsinghua University (Science and Technology), 1998, 38(Supplement 2) : 19-23 (in Chinese) (冯嘉礼,詹 濛.感觉数据-特性抽取的定性映射模型. 清华大学学报(自然科学版), 1998, 38(增刊2): 19-23) [9] Feng J L, Zhan M. Several Relationship Construction among Sensation Mappings. Computer Engineering and Science, 1999, 21(2): 1-5 (in Chinese) (冯嘉礼,詹 濛.感觉诸映射间的关系结构.计算机工程与科学, 1999, 21(2): 1-6) [10] Feng J L. A Kind of Fuzzy Degree Function and Artificial Neurons Induced by Qualitative Mapping. Journal of Nanjing University, 2003, 39(2): 172-181 (in Chinese) (冯嘉礼.定性映射诱导的模糊神经元.南京大学学报, 2003, 39(2): 172-181) [11] Feng J L. Degree Functions and Fuzzy Artificial Neurons Induced by Qualitative Mapping. In: Proc of the International Conference on Fuzzy Information Processing Theory and Application. Beijing, China: Tsinghua University Press, 2003, 511-517 [12] Feng J L, Wu Z X. Conversion Degree Functions Induced by Qualitative Mapping and Artificial Neurons. In: Proc of the 2nd International Conference on Machine Learning and Cybernetics. Xi’an, China, 2003, 1135-1140 [13] Feng J L, Nie W L. Qualitative Mapping Model of Judgment and Recognition Classifying (I). Journal of Guangxi Normal University (Natural Science Edition), 2004, 22(1): 27-32 (in Chinese) (冯嘉礼, 聂文龙.判断的定性映射模型与非线性模式分类(I).广西师范大学学报(自然科学版), 2004, 22(1): 27-32) [14] Feng J L. Qualitative Mapping Model of Judgment and Recognition (II). Journal of Guangxi Normal University(Natural Science Edition), 2004, 22(2): 14-18 (in Chinese) (冯嘉礼.基于定性映射的模式识别方法(II).广西师范大学学报(自然科学版), 2004, 22(2): 14-18) [15] Feng J L, et al. Criterion Transformation in Sensation and Judgment and It’s Analysis Method of Attribute Coordinate System. Guangxi Science, 1994, 4(1): 6-13,22 (in Chinese) (冯嘉礼,等.感知与判断中的基准变换及其性质坐标分析法.广西科学, 1994, 4(1): 6-13,22) [16] Feng J L. A Principle for Constructing Attribute Reasoning Knowledge Base. Computer Research and Development, 1987, 24(11): 55-61(in Chinese) (冯嘉礼.以属性为基础的知识库建库原则. 计算机研究与发展, 1987, 24(11): 56-61) [17] Feng J L. Attribute Theory Methods for Thinking Construction and Intelligence Simulation. Beijing, China: Atomic Press, 1999 (in Chinese) (冯嘉礼.思维与智能科学中的性质论方法.北京: 原子能出版社, 1990) [18] Wu Q F, Feng J L, et al. A Kind of Valuation and Decision Model Based on Analysis and Learning of Attribute Coordinate. Journal of Nanjing University, 2003, 19(2):182-188 (in Chinese) (吴钦藩,冯嘉礼,等.基于属性坐标分析和学习的评估决策模型.南京大学学报, 2003, 39(2): 182-188) [19] Feng J L. The Research on Decision Supports System of Nuclear Accident Emergency and Its Computer Realization, Ph.D Dissertation. Chinese Institute of Atomic Energy, Beijing, 2001 (in Chinese) (冯嘉礼.核事故应急决策支持系统及其计算机实现研究. 博士学位论文.中国原子能科学研究院, 北京, 2001) [20] Feng J L, Lu N. A Multi-Attribute Evaluating Approach Based on Analysis and Learning of Attribute Coordinate. In: Pierre D R, Nachtegael D M, Kerre E E, eds. Computational Intelligence. Singapore, Singapore: World Scientific Publishing, 2004,148-152 [21] Li W P. A Chinese Written Characters Recognition System Based on Qualitative Mapping and Conversion Degree Function. Master Dissertation. Department of Computer Science, Shanghai Maritime University, 2004 (in Chinese) (李文佩.基于定性映射和转化程度函数的汉字识别. 硕士学位论文.上海海事大学,计算机系,上海, 2004) [22] Wang H, Feng J L. Stock Prediction Based on Attribute Thought. Journal of Fudan University(Natural Science), 2004, 43(5): 941-943 (in Chinese) (王 洪,冯嘉礼.基于属性论方法的股市预测算法.复旦大学学报(自然科学版), 2004, 43(5): 941-943) [23] Fang H F. A Kind of Model for Speech Recognition Based on Qualitative Mapping and Conversion Degree Function. Master Dissertation. Department of Computer Science, Shanghai Maritime University, 2004(in Chinese) (方红峰.基于定性映射和转化程度函数的语音识别.硕士学位论文.上海海事大学,计算机系, 上海, 2004) [24] Jiang X Q, Feng J L, et al. A Research and Development of Fingerprint Recognition System Based on Qualitative Mapping and Conversion Degree Function. In: Proc of the 13th Chinese Conference on Artificial Neural Network. Beijing, China: People’s Post and Communication Press, 2003, 265-273 (in Chinese) (蒋晓谦,冯嘉礼,等.基于定性映射和转化程度函数的指纹识别系统研究与开发.见:中国人工神经网络委员会第十三届年会论文集. 北京:人民邮电出版社, 2003, 265-273) [25] Xie Y J. A New Methods for Solving Traveling Salesman Problem(TSP) Based on Qualitative Mapping and Conversion Degree Function. Master Dissertation. Department of Computer Science, Shanghai Maritime University, 2004 (in Chinese) (谢意军.基于定性映射和转化程度函数的TSP问题新方法.硕士学位论文.上海海事大学,计算机系,上海, 2004) [26] Liao X Y. Design and Realization of Network Attacking Detection System Based on Qualitative Mapping. Master Dissertation. Department of Computer Science, Shanghai Maritime University, 2004 (in Chinese)
2006, Vol. 19 
