基于中介逻辑的模糊信息处理的研究
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摘要
在现代社会里,模糊信息处理广泛涉及生产、生活的各个领域。由中国学者创立的中介逻辑,作为目前国内外唯一区分否定中的矛盾与对立、肯定一些对立概念间存在中介对象的形式化逻辑系统,在纯数学基础理论意义下,实现了数学研究对象由精确性量性对象到模糊性对象的再扩充。因而,如何运用中介逻辑基本思想和理论研究处理模糊信息,是一个富有新意的研究工作。
本文第一章介绍了目前学者们关于信息领域中否定关系的研究;第二章从概念本质上区分知识的矛盾否定与对立否定,介绍了清晰概念中的两种否定关系和模糊概念中的三种否定关系,即“矛盾”否定、“对立”否定和“中介”否定;第三章介绍了中介逻辑的思想背景与基本理论,及基于中介逻辑系统的无穷值语义模型的形式化描述,并且对于现有逻辑理论处理否定知识的能力进行了比较。
第四章基于中介逻辑思想与距离测度,以中介真值程度函数为工具,建立了模糊评判矩阵,并综合评判因素中肯定信息与否定信息的真值程度确立评判指数,进而以评判指数作为总体评判的数量依据,对评判对象进行比较,从而建立了一种新的模糊评判模型;最后讨论了它在一个具体的模糊评判实例中的应用。
模糊语言变量的量化是否合理直接关系着基于这些变量的模糊推理结果是否更符合客观现实。第五章基于模糊语言变量的语义和中介无穷值语义模型的思想,采用距离比率函数通过引入参数提出了一种新的模糊语气算子,并且通过实例加以说明分析。
针对具体处理模糊知识的需要,第六章首先改进了中介无穷值语义模型,对其进行了语义描述;在此基础上扩展了Zadeh提出的近似推理方法即CRI算法,给出了基于中介逻辑思想的区分矛盾否定和对立否定的一种更为具体的算法,通过一具体的例子进行应用分析,同时扩展了语义匹配度的度量,包括语义距离和相似度。
Fuzzy information processing is widely involved in the production and lives in the modern society. Medium logic, established by Chinese scholars, is a formal logic system for differentiating contradictory negation from opposite negation and implies that there exist some medium objects between some opposite concepts, which realize the extention from exact objects to fuzzy objects. Therefor it is a useful work that how to put the medium logic theoery into fuzzy information prosessing.
In chapter 1, the paper mainly introduces the research results about negative relation of fuzzy information currently. In chapter 2, it makes an introduction of concept essence of negative knowledge, as consideres that negations in distinct knowledge includes two kinds and there are three kinds of negative relations about fuzzy knowledge, namely Contradictory negation, Opposite negation and Medium negation. In chapter 3, firstly it introduces the basic theoery and background of medium logic, then provides its interpretation of infinite-valued modle and gives both semantic and logic description. In the last part of the chapter, we also present the disadvantages of the current logic for processing the negative relations.
Based on medium logic and distance measure, fuzzy evalution matrix is established with medium truth rade function in chapter 4, and the index of fuzzy evalution is educed by considering positive information and negative information of fuzzy evalution factors. Then the evaluation objects are compared by the evaluation index which is regarded as the basis of comprehensive evaluation. Therefore a new kind of fuzzy comprehensive evaluation model is constructed, the application of which is discussed by an example in the end of the paper.
Whether the quantization of fuzzy linguistic variables is reasonable is directly associate with rationality of fuzzy reasoning results. Chapter 5 firstly gives individual truth grade function adopting distance ration function based on the semanic of fuzzy linguistic variables and the background of medium logic, then proposes a new fuzzy tone operator in virtue of the notion of infinite valued semanic model for medium predicate logic, which is put into a special example for discussing finally.
Medium logic completely reflects both opposite relation and contradictory relation. Chapter 6 first improves the infinite-valued semantic model of medium logic and then puts a semantic interpretation. After that it expands the CRI algorithm bought forward by Zadeh, and obtains another algorithm based on the notion of medium logic. Meanwhile the semantic match degree including semantic similarity and semantic distance are put forward.A special example validates the rationality of the extended algorithm at last.
本文第一章介绍了目前学者们关于信息领域中否定关系的研究;第二章从概念本质上区分知识的矛盾否定与对立否定,介绍了清晰概念中的两种否定关系和模糊概念中的三种否定关系,即“矛盾”否定、“对立”否定和“中介”否定;第三章介绍了中介逻辑的思想背景与基本理论,及基于中介逻辑系统的无穷值语义模型的形式化描述,并且对于现有逻辑理论处理否定知识的能力进行了比较。
第四章基于中介逻辑思想与距离测度,以中介真值程度函数为工具,建立了模糊评判矩阵,并综合评判因素中肯定信息与否定信息的真值程度确立评判指数,进而以评判指数作为总体评判的数量依据,对评判对象进行比较,从而建立了一种新的模糊评判模型;最后讨论了它在一个具体的模糊评判实例中的应用。
模糊语言变量的量化是否合理直接关系着基于这些变量的模糊推理结果是否更符合客观现实。第五章基于模糊语言变量的语义和中介无穷值语义模型的思想,采用距离比率函数通过引入参数提出了一种新的模糊语气算子,并且通过实例加以说明分析。
针对具体处理模糊知识的需要,第六章首先改进了中介无穷值语义模型,对其进行了语义描述;在此基础上扩展了Zadeh提出的近似推理方法即CRI算法,给出了基于中介逻辑思想的区分矛盾否定和对立否定的一种更为具体的算法,通过一具体的例子进行应用分析,同时扩展了语义匹配度的度量,包括语义距离和相似度。
Fuzzy information processing is widely involved in the production and lives in the modern society. Medium logic, established by Chinese scholars, is a formal logic system for differentiating contradictory negation from opposite negation and implies that there exist some medium objects between some opposite concepts, which realize the extention from exact objects to fuzzy objects. Therefor it is a useful work that how to put the medium logic theoery into fuzzy information prosessing.
In chapter 1, the paper mainly introduces the research results about negative relation of fuzzy information currently. In chapter 2, it makes an introduction of concept essence of negative knowledge, as consideres that negations in distinct knowledge includes two kinds and there are three kinds of negative relations about fuzzy knowledge, namely Contradictory negation, Opposite negation and Medium negation. In chapter 3, firstly it introduces the basic theoery and background of medium logic, then provides its interpretation of infinite-valued modle and gives both semantic and logic description. In the last part of the chapter, we also present the disadvantages of the current logic for processing the negative relations.
Based on medium logic and distance measure, fuzzy evalution matrix is established with medium truth rade function in chapter 4, and the index of fuzzy evalution is educed by considering positive information and negative information of fuzzy evalution factors. Then the evaluation objects are compared by the evaluation index which is regarded as the basis of comprehensive evaluation. Therefore a new kind of fuzzy comprehensive evaluation model is constructed, the application of which is discussed by an example in the end of the paper.
Whether the quantization of fuzzy linguistic variables is reasonable is directly associate with rationality of fuzzy reasoning results. Chapter 5 firstly gives individual truth grade function adopting distance ration function based on the semanic of fuzzy linguistic variables and the background of medium logic, then proposes a new fuzzy tone operator in virtue of the notion of infinite valued semanic model for medium predicate logic, which is put into a special example for discussing finally.
Medium logic completely reflects both opposite relation and contradictory relation. Chapter 6 first improves the infinite-valued semantic model of medium logic and then puts a semantic interpretation. After that it expands the CRI algorithm bought forward by Zadeh, and obtains another algorithm based on the notion of medium logic. Meanwhile the semantic match degree including semantic similarity and semantic distance are put forward.A special example validates the rationality of the extended algorithm at last.
引文
1. L A Zadeh. Fuzzy Sets [J]. Inform And Control, 1965, Vol 8: 338-353
2. K Atanassov. Intuitionistic Fuzzy Sets[J]. Fuzzy Sets and Systems, 1986, 20(1): 87-96
3. R R Yanger. Connectives and Quantifiers in Fuzzy Sets[J]. Fuzzy Sets and Systems, 1991, 40(1): 39-75
4. Gau Wen-Lung, D J Buehrer. Vague sets[C]. IEEE Transactions on Systems Man and Cybernetics, 1993, 23 (2): 610-614
5. Z Pawlak. Rough Sets[J]. International Journal of Computer and Information Sciences, 1982 (11): 341-356
6朱梧槚,肖奚安.数学基础概论[M].南京:南京大学出版社,1996.192-193, 237-243,248-367,383-493
7. Gerd Wagner. Partial logics with two kinds of negation as a foundation for knowledge-based reasoning[C]. In: D Gabbay and H Wansing, eds. What Is Negation. Oxford: Oxford University Press, 1999.1-35.
8. Gerd Wagner. A Database Needs Two Kinds of Negation[C]. In: B.Thalbeim, J Demetrovics, H-D Gerhardt, eds. Proc of 3rd Symposium on Mathematical Fundamentals of Database and Knowledge Bases Systems(MFDBS). Heidelberg: Springer-Verlag, 1991. 357-371
9. Gerd Wagner.Vivid Logic: Knowledge-Based Reasoning with Two Kinds of Negation[J], Heidelberg: Springer Verlag, 1994.89-110
10. Gerd Wagner. Web rules need two kinds of negation[C]. In: F Bry, N Henze, and J Maluszynski, eds. Proc of the 1st international workshop on Principles and Practice of Semantic Web Reasoning (PPSW3’03). Heidelberg: Springer Verlag, 2003.33-50
11. K Kaneiwa. Negations in description logic - contraries, contradictories, and subcontraries[C]. In: F. Dau, M.-L. Mugnier, and G. Stumme, eds. Contributions to ICCS2005. Kassel: Kassel University Press, 2005. 66–79
12. S′ebastien Ferré. Negation, Opposition, and Possibility in Logical Concept Analysis[C]. In: B Ganter and L Kwuida, eds. ICFCA2006, LNAI 3874. Heidelberg: Springer, 2006.130-145
13. Pan Zheng-hua, Zhu Wu-jia. A new cognition and processing on contradictory knowledge[C]. IEEE- Proceedings of 2006 International Conference on Machine Learning and Cybernetics. VOLS 1-7, 2006. 1532-1537
14. Zhenghua Pan, Shengli Zhang, Differentiation and Processing on Contradictory Relationand Opposite Relation in Knowledge[C], Proc.of IEEE-The 3rd International Conference on Natural Computation (ICNC’07), Vol.4, 2007, 334-338
15. Pan Zheng-hua. Five Kinds of Contradictory Relations and Opposite Relations in Inconsistent Knowledge[C]. Proceedings of IEEE-Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD’07). Washington: IEEE Computer Society, 2007. Vol 4, 761-764
16. Zhenghua Pan, A Logic Description on Different Negation Relation in Knowledge[J], LNCS, Vol.5227, Springer Berlin / Heidelberg, 2008: 815-823
17.潘正华.知识中不同否定关系的一种逻辑描述[J].自然科学进展, 2008, 18(11): 66-74
18. Cen Wang, Zhenghua Pan, Searching method of fuzzy knowledge reasoning based medium logic[J], Lecture Notes in Computer Science, Vol.5227, Springer Berlin/Heidelberg, 2008: 401-409
19. Zhenghua Pan, Cen Wang, Representation and Reasoning Algorithm About Fuzzy Knowledge and Its Three kinds of Negations[C], The 2nd IEEE International Conference on Advanced Computer Control (ICACC 2010), Volume, 2, 2010, 603-607
20.王岑,潘正华,程天笑.基于中介逻辑的模糊知识推理的搜索处理[J].计算机工程与应用,2009,45(21): 175-178
21.王岑,潘正华.基于中介逻辑的模糊知识表示及应用[J].计算机工程与科学, 2008,30(11): 80-84
22.程天笑,潘正华,王岑.基于中介逻辑的近似推理[J].计算机工程与科学,2009, 45(21): 163-166
23. Zhenghua Pan, FUZZY SET WITH THREE KINDS OF NEGATIONS IN FUZZY KNOWLEDGE PROCESSING[C]. 2010 International Conference of Machine Learning and Cybernetics (ICMLC2010)
24. Zhu Wu-Jia, Xiao Xi-An. Propositional calculus system of medium logic(I)[J]. Nature Magazine, 1985 (8): 315-316
25. Zhu Wu-jia, Xiao Xi-an. On the Naive Mathematical Models of Medium Mathematical System [J]. J Math Res & Exposition, 1988 (1): 139-151
26. Wujia Zhu,Xian Xiao. Predicate Calculus System of Medium Logic[J]. Journal of Nanjing University,1988,24(7):35-46
27.潘正华.中介谓词逻辑系统的λ-归[J].软件学报, 2003,14(3): 345~349
28. Pan Zheng-hua, Zhu Wu-jia. A finite and infinite-valued model of the medium proposition logic[C]. In: H. Zhiqiu, S.Guohua, W.Chuandong, eds. Proc of the SecondAsian Workshop on Foundations of Software. Nanjing: Southeast University Press, 2003. 103-106
29. Zheng-hua Pan, Wu-jia Zhu, An interpretation of infinite valued for medium proposition logic[C].Proc.of IEEE-Third International Conference on Machine Learning and Cybernetics, 2004,14(7) 2495-2499
30.洪龙,肖奚安,朱梧槚.中介真值程度的度量及应用(Ι)[J].计算机学报,2006,29(12): 2186-2193
31.洪龙,肖奚安,朱梧槚.中介真值程度的度量及其应用(II)[J].计算机学报, 2007,30(9): 1551-1558
32.汪培庄,韩立岩.应用模糊数学[M].北京:北京经济学院出版社, 1989.147-167
33.陆钟万.面向计算机科学的数理逻辑[M].北京:科学出版社,2002.78-103,225-227
34.陆建江,张亚非等.语义网原理与技术[M].北京:科学出版社,2007.88-93
35.曹谢东.模糊信息处理及应用[M].北京:科学出版社, 2003.43-46, 57-80
36.张家龙.数理逻辑发展史—从莱布尼茨到哥德尔[M].北京:社会科学文献出版社,1993.115?117
37.陈水利,李敬功,王向公.模糊集理论及应用[M].北京:科学出版社, 2005.191-201,373-391
38.梁保松,曹殿立.模糊数学及其应用[M].北京:科学出版社, 2007.131-151
39.刘林,曹艳平,王婷,李娟飞.应用模糊数学[M].陕西科学技术出版社, 2008. 156-158,
40. Zadeh,L.A. , The concept of a linguistic variable and its application to approximate reasoning.Information Science.1975(8): 199-249
41.吴望名.模糊推理的原理和方法[M].贵州科技出版社, 1991.190-210
42. Baldwin,.J.F., A new approach to approximate reasoning using a fuzzy logic, FSS(1979):309-325
43. Wang,P.z. and Zhang,H.M. , Truth-valued flow inference and its dynamic analysis.Journal of Beijing Normal University, 1989,No.1
44.王士同.模糊推理理论与模糊专家系统[M].上海科学技术文献出版社, 1994.47-51,79-89
45.王国俊.模糊推理的全蕴涵三I算法[J].中国科学(E辑),1999 (1): 43-53
46.刘峡壁.人工智能导轮—方法与系统[M].北京:国防工业出版社, 2008.112-116
2. K Atanassov. Intuitionistic Fuzzy Sets[J]. Fuzzy Sets and Systems, 1986, 20(1): 87-96
3. R R Yanger. Connectives and Quantifiers in Fuzzy Sets[J]. Fuzzy Sets and Systems, 1991, 40(1): 39-75
4. Gau Wen-Lung, D J Buehrer. Vague sets[C]. IEEE Transactions on Systems Man and Cybernetics, 1993, 23 (2): 610-614
5. Z Pawlak. Rough Sets[J]. International Journal of Computer and Information Sciences, 1982 (11): 341-356
6朱梧槚,肖奚安.数学基础概论[M].南京:南京大学出版社,1996.192-193, 237-243,248-367,383-493
7. Gerd Wagner. Partial logics with two kinds of negation as a foundation for knowledge-based reasoning[C]. In: D Gabbay and H Wansing, eds. What Is Negation. Oxford: Oxford University Press, 1999.1-35.
8. Gerd Wagner. A Database Needs Two Kinds of Negation[C]. In: B.Thalbeim, J Demetrovics, H-D Gerhardt, eds. Proc of 3rd Symposium on Mathematical Fundamentals of Database and Knowledge Bases Systems(MFDBS). Heidelberg: Springer-Verlag, 1991. 357-371
9. Gerd Wagner.Vivid Logic: Knowledge-Based Reasoning with Two Kinds of Negation[J], Heidelberg: Springer Verlag, 1994.89-110
10. Gerd Wagner. Web rules need two kinds of negation[C]. In: F Bry, N Henze, and J Maluszynski, eds. Proc of the 1st international workshop on Principles and Practice of Semantic Web Reasoning (PPSW3’03). Heidelberg: Springer Verlag, 2003.33-50
11. K Kaneiwa. Negations in description logic - contraries, contradictories, and subcontraries[C]. In: F. Dau, M.-L. Mugnier, and G. Stumme, eds. Contributions to ICCS2005. Kassel: Kassel University Press, 2005. 66–79
12. S′ebastien Ferré. Negation, Opposition, and Possibility in Logical Concept Analysis[C]. In: B Ganter and L Kwuida, eds. ICFCA2006, LNAI 3874. Heidelberg: Springer, 2006.130-145
13. Pan Zheng-hua, Zhu Wu-jia. A new cognition and processing on contradictory knowledge[C]. IEEE- Proceedings of 2006 International Conference on Machine Learning and Cybernetics. VOLS 1-7, 2006. 1532-1537
14. Zhenghua Pan, Shengli Zhang, Differentiation and Processing on Contradictory Relationand Opposite Relation in Knowledge[C], Proc.of IEEE-The 3rd International Conference on Natural Computation (ICNC’07), Vol.4, 2007, 334-338
15. Pan Zheng-hua. Five Kinds of Contradictory Relations and Opposite Relations in Inconsistent Knowledge[C]. Proceedings of IEEE-Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD’07). Washington: IEEE Computer Society, 2007. Vol 4, 761-764
16. Zhenghua Pan, A Logic Description on Different Negation Relation in Knowledge[J], LNCS, Vol.5227, Springer Berlin / Heidelberg, 2008: 815-823
17.潘正华.知识中不同否定关系的一种逻辑描述[J].自然科学进展, 2008, 18(11): 66-74
18. Cen Wang, Zhenghua Pan, Searching method of fuzzy knowledge reasoning based medium logic[J], Lecture Notes in Computer Science, Vol.5227, Springer Berlin/Heidelberg, 2008: 401-409
19. Zhenghua Pan, Cen Wang, Representation and Reasoning Algorithm About Fuzzy Knowledge and Its Three kinds of Negations[C], The 2nd IEEE International Conference on Advanced Computer Control (ICACC 2010), Volume, 2, 2010, 603-607
20.王岑,潘正华,程天笑.基于中介逻辑的模糊知识推理的搜索处理[J].计算机工程与应用,2009,45(21): 175-178
21.王岑,潘正华.基于中介逻辑的模糊知识表示及应用[J].计算机工程与科学, 2008,30(11): 80-84
22.程天笑,潘正华,王岑.基于中介逻辑的近似推理[J].计算机工程与科学,2009, 45(21): 163-166
23. Zhenghua Pan, FUZZY SET WITH THREE KINDS OF NEGATIONS IN FUZZY KNOWLEDGE PROCESSING[C]. 2010 International Conference of Machine Learning and Cybernetics (ICMLC2010)
24. Zhu Wu-Jia, Xiao Xi-An. Propositional calculus system of medium logic(I)[J]. Nature Magazine, 1985 (8): 315-316
25. Zhu Wu-jia, Xiao Xi-an. On the Naive Mathematical Models of Medium Mathematical System [J]. J Math Res & Exposition, 1988 (1): 139-151
26. Wujia Zhu,Xian Xiao. Predicate Calculus System of Medium Logic[J]. Journal of Nanjing University,1988,24(7):35-46
27.潘正华.中介谓词逻辑系统的λ-归[J].软件学报, 2003,14(3): 345~349
28. Pan Zheng-hua, Zhu Wu-jia. A finite and infinite-valued model of the medium proposition logic[C]. In: H. Zhiqiu, S.Guohua, W.Chuandong, eds. Proc of the SecondAsian Workshop on Foundations of Software. Nanjing: Southeast University Press, 2003. 103-106
29. Zheng-hua Pan, Wu-jia Zhu, An interpretation of infinite valued for medium proposition logic[C].Proc.of IEEE-Third International Conference on Machine Learning and Cybernetics, 2004,14(7) 2495-2499
30.洪龙,肖奚安,朱梧槚.中介真值程度的度量及应用(Ι)[J].计算机学报,2006,29(12): 2186-2193
31.洪龙,肖奚安,朱梧槚.中介真值程度的度量及其应用(II)[J].计算机学报, 2007,30(9): 1551-1558
32.汪培庄,韩立岩.应用模糊数学[M].北京:北京经济学院出版社, 1989.147-167
33.陆钟万.面向计算机科学的数理逻辑[M].北京:科学出版社,2002.78-103,225-227
34.陆建江,张亚非等.语义网原理与技术[M].北京:科学出版社,2007.88-93
35.曹谢东.模糊信息处理及应用[M].北京:科学出版社, 2003.43-46, 57-80
36.张家龙.数理逻辑发展史—从莱布尼茨到哥德尔[M].北京:社会科学文献出版社,1993.115?117
37.陈水利,李敬功,王向公.模糊集理论及应用[M].北京:科学出版社, 2005.191-201,373-391
38.梁保松,曹殿立.模糊数学及其应用[M].北京:科学出版社, 2007.131-151
39.刘林,曹艳平,王婷,李娟飞.应用模糊数学[M].陕西科学技术出版社, 2008. 156-158,
40. Zadeh,L.A. , The concept of a linguistic variable and its application to approximate reasoning.Information Science.1975(8): 199-249
41.吴望名.模糊推理的原理和方法[M].贵州科技出版社, 1991.190-210
42. Baldwin,.J.F., A new approach to approximate reasoning using a fuzzy logic, FSS(1979):309-325
43. Wang,P.z. and Zhang,H.M. , Truth-valued flow inference and its dynamic analysis.Journal of Beijing Normal University, 1989,No.1
44.王士同.模糊推理理论与模糊专家系统[M].上海科学技术文献出版社, 1994.47-51,79-89
45.王国俊.模糊推理的全蕴涵三I算法[J].中国科学(E辑),1999 (1): 43-53
46.刘峡壁.人工智能导轮—方法与系统[M].北京:国防工业出版社, 2008.112-116