【作者】 张丽珍；

【导师】 潘正华；

【作者基本信息】 江南大学 ， 应用数学， 2010， 硕士

【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。更多还原

【Abstract】 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.更多还原