模糊推理方法及模糊逻辑形式系统研究
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摘要
1965年,Zadeh教授提出了模糊集的概念。从那时起,模糊推理理论得到了迅猛的发展,在理论与应用两方面的研究成果层出不穷。现在,已经诞生了几百种模糊推理方法,它们都从不同方面不同程度地改进和改善了模糊推理理论,却很难改变模糊推理的逻辑基础不严格的现状。究其原因,这与模糊推理理论发展至今却还没有一个公认的系统化的评价标准不无关系。但由于模糊推理的多样性和复杂性,一个公认标准的制定不可能一蹴而就,而是需要长期的探索和研究。
模糊推理方法的重要性质有很多,其中,还原性是对模糊推理方法最基本的要求,也是研究得最多的模糊推理方法的重要性质之一。虽然在还原性方面已有诸多研究成果,但至今为止仍没有对模糊推理方法还原性的系统性研究成果。作为模糊推理方法最重要的性质和公认的基本要求,有必要对常用模糊推理方法在各种情况下的还原性进行全面系统的研究,再根据研究结果,改进现有模糊推理方法,或是提出新的性能更好的模糊推理方法。这对制定一个合理的评价模糊推·理方法的统一标准,完善模糊推理方法的逻辑基础,都是相当重要的。在另一方面,逻辑与推理密不可分,模糊逻辑自身价值的体现主要取决于模糊逻辑系统所具有的推理能力。因此,除了对模糊推理方法的研究,研究其相应的模糊逻辑形式系统也是十分必要的。
本论文的主要研究内容是,以几种最具代表性的模糊推理方法：CRI方法、三Ⅰ算法、真值流推理方法和AARS算法为例,对模糊推理方法的还原性进行了全面系统的研究,并总结了影响模糊推理方法还原性的因素,再根据系统研究还原性的结论,提出一种具有还原性的模糊推理方法。首先,介绍了模糊推理中重要的模糊集合运算和蕴涵算子的性质,总结了模糊推理模型的类型和多种解决方法。其次,以几种常见模糊推理方法为代表,对各种模糊推理方法的是否具有还原性进行了系统研究,并总结了影响模糊推理方法还原性的因素。然后,根据前面的研究成果,提出一种新的具有还原性的相似度算法,证明了该新算法的还原性,还提供了比较新算法与CRI方法、AARS算法推理结果和模糊系统逼近性的实验图像。最后,建立了一个与新算法相对应的模糊逻辑形式系统。
基于目前模糊逻辑与模糊推理的亟待解决的问题,本论文在模糊逻辑已经取得诸多成果的大背景下,结合经典逻辑和非经典逻辑研究的一般方法,对模糊逻辑的演算和推理进行深入研究,希望能为今后的研究工作奠定坚实的基础。
The theory of fuzzy reasoning has made a great development, and got good results in application since the concept of fuzzy sets was first introduced by Zadeh in 1965. Up to now, there exist a lot of fuzzy reasoning methods. Those methods made successful improvement in various research fields of theory and application, but took little effect on providing more reasonable logic foundation for fuzzy reasoning. This problem is due in part to there is no any universal criterion to judge all those fuzzy reasoning methods good or not. Otherwize, a universal criterion cannot be expected overnight because of the diversity and complexity of fuzzy reasoning, it requires a long-time research.
There are many important properties of fuzzy reasoning methods, among them, the property of being consistent is most important and has been most noticed. Now, consistency is the most important one criterion of fuzzy reasoning methods accepted by most people. Formerly although many scholars have studied the property of being consistent, they have regarded the property as one kind of fuzzy reasoning and lack of essentially conducted the contrast research. So as the most important one criterion of fuzzy reasoning methods, it is necessary to study the consistency of fuzzy reasoning methods from every side. Furthermore, improve the existing fuzzy reasoning methods, or propose a new excellent fuzzy reasoning method, base on a comprehensive summary of the existing research.h outcomes. Those outcomes can provide a basis for a universal criterion. Otherwize, reasoning is inseparable from logic. The reasoning capacities of formal logic systems also play a major role in fuzzy theory. It is necessary to study depthly on fuzzy logic formal systems while studing on fuzzy reasoning methods.
In this paper, the properties of being consistent of the existing fuzzy reasoning methods are essentially contrast researched, especially the four methods:Zadeh's CRI method, Wang's Triple I Method, Truth-Valued flow method and Turksen et al.'s AARS method, then a conclusion that the consistency of a fuzzy reasoning method is correlative with its reasoning mechanism is introduced, and a consistent based on similarity measure with thresholds is proposed based on the conclusion. Detailedly, first the major computations between fuzzy sets and implication operators are introduced, and the kinds of fuzzy reasoning forms are summarized. Then the definitions of the consistency of GMP and GMT with thresholds are proposed, and some examples are given to show that the existing fuzzy reasoning methods are almost not consistent for multiple rules. Consequently, a consistent fuzzy reasoning algorithm based on similarity measure with thresholds is proposed, which is proved to be consistent for multiple rules in this paper. Some results are given to show that the consistent fuzzy reasoning algorithm based on similarity measure with thresholds is workable. Finally, a fuzzy logic formal system and its dual formal system are established.
In view of the problems about fuzzy logic and fuzzy reasoning, a thorough study are made on fuzzy reasoning methods and their logic foundations。The study results in this paper are expected to improve and perfect fuzzy theory to a certain degree, and lay a solid foundation in following research.
模糊推理方法的重要性质有很多,其中,还原性是对模糊推理方法最基本的要求,也是研究得最多的模糊推理方法的重要性质之一。虽然在还原性方面已有诸多研究成果,但至今为止仍没有对模糊推理方法还原性的系统性研究成果。作为模糊推理方法最重要的性质和公认的基本要求,有必要对常用模糊推理方法在各种情况下的还原性进行全面系统的研究,再根据研究结果,改进现有模糊推理方法,或是提出新的性能更好的模糊推理方法。这对制定一个合理的评价模糊推·理方法的统一标准,完善模糊推理方法的逻辑基础,都是相当重要的。在另一方面,逻辑与推理密不可分,模糊逻辑自身价值的体现主要取决于模糊逻辑系统所具有的推理能力。因此,除了对模糊推理方法的研究,研究其相应的模糊逻辑形式系统也是十分必要的。
本论文的主要研究内容是,以几种最具代表性的模糊推理方法：CRI方法、三Ⅰ算法、真值流推理方法和AARS算法为例,对模糊推理方法的还原性进行了全面系统的研究,并总结了影响模糊推理方法还原性的因素,再根据系统研究还原性的结论,提出一种具有还原性的模糊推理方法。首先,介绍了模糊推理中重要的模糊集合运算和蕴涵算子的性质,总结了模糊推理模型的类型和多种解决方法。其次,以几种常见模糊推理方法为代表,对各种模糊推理方法的是否具有还原性进行了系统研究,并总结了影响模糊推理方法还原性的因素。然后,根据前面的研究成果,提出一种新的具有还原性的相似度算法,证明了该新算法的还原性,还提供了比较新算法与CRI方法、AARS算法推理结果和模糊系统逼近性的实验图像。最后,建立了一个与新算法相对应的模糊逻辑形式系统。
基于目前模糊逻辑与模糊推理的亟待解决的问题,本论文在模糊逻辑已经取得诸多成果的大背景下,结合经典逻辑和非经典逻辑研究的一般方法,对模糊逻辑的演算和推理进行深入研究,希望能为今后的研究工作奠定坚实的基础。
The theory of fuzzy reasoning has made a great development, and got good results in application since the concept of fuzzy sets was first introduced by Zadeh in 1965. Up to now, there exist a lot of fuzzy reasoning methods. Those methods made successful improvement in various research fields of theory and application, but took little effect on providing more reasonable logic foundation for fuzzy reasoning. This problem is due in part to there is no any universal criterion to judge all those fuzzy reasoning methods good or not. Otherwize, a universal criterion cannot be expected overnight because of the diversity and complexity of fuzzy reasoning, it requires a long-time research.
There are many important properties of fuzzy reasoning methods, among them, the property of being consistent is most important and has been most noticed. Now, consistency is the most important one criterion of fuzzy reasoning methods accepted by most people. Formerly although many scholars have studied the property of being consistent, they have regarded the property as one kind of fuzzy reasoning and lack of essentially conducted the contrast research. So as the most important one criterion of fuzzy reasoning methods, it is necessary to study the consistency of fuzzy reasoning methods from every side. Furthermore, improve the existing fuzzy reasoning methods, or propose a new excellent fuzzy reasoning method, base on a comprehensive summary of the existing research.h outcomes. Those outcomes can provide a basis for a universal criterion. Otherwize, reasoning is inseparable from logic. The reasoning capacities of formal logic systems also play a major role in fuzzy theory. It is necessary to study depthly on fuzzy logic formal systems while studing on fuzzy reasoning methods.
In this paper, the properties of being consistent of the existing fuzzy reasoning methods are essentially contrast researched, especially the four methods:Zadeh's CRI method, Wang's Triple I Method, Truth-Valued flow method and Turksen et al.'s AARS method, then a conclusion that the consistency of a fuzzy reasoning method is correlative with its reasoning mechanism is introduced, and a consistent based on similarity measure with thresholds is proposed based on the conclusion. Detailedly, first the major computations between fuzzy sets and implication operators are introduced, and the kinds of fuzzy reasoning forms are summarized. Then the definitions of the consistency of GMP and GMT with thresholds are proposed, and some examples are given to show that the existing fuzzy reasoning methods are almost not consistent for multiple rules. Consequently, a consistent fuzzy reasoning algorithm based on similarity measure with thresholds is proposed, which is proved to be consistent for multiple rules in this paper. Some results are given to show that the consistent fuzzy reasoning algorithm based on similarity measure with thresholds is workable. Finally, a fuzzy logic formal system and its dual formal system are established.
In view of the problems about fuzzy logic and fuzzy reasoning, a thorough study are made on fuzzy reasoning methods and their logic foundations。The study results in this paper are expected to improve and perfect fuzzy theory to a certain degree, and lay a solid foundation in following research.
引文
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