直觉模糊推理系统的鲁棒性

强调模糊性和疑惑性的Atanassov直觉模糊集在决策、图像处理、聚类和专家系统等智能系统中得以广泛的应用。为了更好地实现直觉模糊推理,研究直觉模糊推理系统诸如鲁棒性的基本性质意义非凡。本文给出了直觉模糊t-模和s-模、否和几种蕴涵(即R-、S-和QL-蕴涵)的灵敏度表达式。并根据这些模糊连接词和直觉模糊集的灵敏度深入分析了直觉模糊推理系统的鲁棒性,并发现直觉模糊推理系统的鲁棒性取决于其构成的直觉模糊连接词。     

模糊推理系统的鲁棒性

主要讨论模糊推理系统的鲁棒性. 给出基于逻辑等价度量的模糊集扰动的定义,讨论模糊集扰动与模糊连接词及蕴涵算子扰动之间的关系,针对若干特殊的模糊连接词及蕴涵算子的扰动情形,给出模糊推理系统的扰动的最佳结果.     

三I算法的鲁棒性

基于三I算法的模糊推理不仅在语义上而且在语构上均有合理的解释。在模糊推理三I算法中,研究输入的微小变化所引起输出变化幅度尤为重要。本文首先给出了基于QL蕴涵的三I算法的表达式,进一步借助模糊连接词的鲁棒性,系统地研究了基于几种常见的蕴涵的三I算法的鲁棒性。     

模糊推理三I算法的逻辑基础

在模糊推理理论中，近期问世的三I推理方法以逻辑蕴涵运算取代传统的合成运算，从根本上改进了传统的合成推理规则(即CRI方法)。本文基于模糊命题逻辑的形式演绎系统L^*和模糊谓词逻辑的一阶系统K^*，构建了一个完备的多型变元一阶系统Kms^*，并且将三I算法完全纳入了模糊逻辑的框架之中，从而为模糊推理奠定了严格的逻辑基础。     

区间值模糊推理的三Ⅰ算法

模糊推理在控制和人工智能等领域已得到了广泛的应用，但其理论基础还不完善，王国俊教授提出的模糊命题逻辑的形式演绎系统和三Ⅰ算法为模糊推理奠定了严格的逻辑基础，本文把三Ⅰ算法用于区间值模糊推理，并且指出一般模糊推理是在区间退化为点时的特殊区间值模糊推理，从而把一般模糊推理纳入于区间值模糊推理的框架之内。     

基于神经网络的模糊推理

为了使模糊推理符合推理原则，目前已定义了１０多种模糊关系，但各种模糊关系定义都存在一定的缺陷。本文提出的基于神经网络的模糊推理，能很好地符合模糊推理原则。     

模糊命题演算系统(L)*的简化与独立性

模糊逻辑命题演算系统L^＊在模糊逻辑与模糊推理的结合研究中得到了成功的应用。本文进一步研究系统L^＊的语法结构，得到了一些有趣的新结果，特别是给出了它的一个简化形式，并证明了这个简化公理系统的独立性。     

基于极大模糊熵原理的模糊推理三I算法

用模糊熵来度量模糊推理结果的模糊程度，并用本文给出的极大模糊熵原理对王国俊先生提出的模糊推理三Ⅰ算法做进一步的解释和改进，提出基于极大模糊熵原理的模糊推理三Ⅰ算法，证明这几种算法在一定条件下是关系再现算法。     

翼伞航迹跟踪多输入模糊控制

本文研究了翼伞系统的自主归航控制技术。采用输入信息少的模糊控制器会影响翼伞的控制精度,而当输入信息较多是会使模糊控制器的模糊规则判断复杂化,影响控制器的反应速度。本文基于因素空间理论,对多输入的翼伞航迹跟踪模糊控制器的模糊推理规则判断进行了简化处理。经简化后的模糊推理机制,在不损失输入信息和不损害模糊控制器的前提下,利用最少的输入信息达到相同的模糊推理结果,大大减小了不必要的模糊推理,降低了模糊控制器的计算负担,大大提高了翼伞航迹跟踪的实时控制效果。仿真结果证明了新方法的有效性。     

基于Schweizer-Sklar算子的模糊推理模型的连续性

本文将Schweizer-Sklar算子引入模糊系统,引入了模糊推理模型连续性的新定义,给出了两种典型的模糊推理模型为连续模型的充要条件.讨论了几种常用的模糊推理模型的连续性,给出其改进形式.     

一种新的三角模糊数算子在加权模糊推理中的应用

针对基于模糊逻辑的加权模糊推理,Chen Shy i-M ing提出了两种计算合取式前件整体真值的方法。由于所用模糊数算子的影响,两种方法的求取结果在准确性和合理性上都存在一定的缺陷。这种缺陷将直接影响推理的性能。因此,为改善这种缺陷,提高推理性能,本文提出了一种新的三角模糊数算子。它的应用可以提高推理的准确性和合理性。     

Generalizing the modeling of fuzzy logic controllers by parameterized aggregation operators

We describe the type of reasoning used in the typical fuzzy logic controller, the Mamdani reasoning method. We point out the basic assumptions in this model. We discuss the S-OWA operators which provide families of parameterized “andlike” and “orlike” operators. We generalize the Mamdani model by introducing these operators. We introduce a method, which we call Direct Fuzzy Reasoning (DFR), which results from one choice of the parameters. We develop some learning algorithms for the new method. We show how the Takagi-Sugeno-Kang (TSK) method of reasoning is an example of this DFR method.     

基于三角范数的模糊逻辑中的三Ⅰ方法

三I推理方法是一种新的模糊推理方法,通过已有的研究成果表明,在许多方面它优于传统的CRI推理方法,它将成为模糊系统和人工智能的理论和应用研究中一个比较理想的推理机制。最近,国外学者提出了一个新的模糊逻辑形式系统,叫做Monoidal t-norm based logics(简记为MTL),已经证明这个形式系统是所有基于左连续三角范数的模糊逻辑的共同形式化。本文基于这类逻辑将三I推理方法形式化,从而在这些逻辑系统中为三推理方法找到了可靠的逻辑依据。     

Symmetric implicational method of fuzzy reasoning

Fuzzy reasoning should take into account the factors of both the logic system and the reasoning model, thus a new fuzzy reasoning method called the symmetric implicational method is proposed, which contains the full implication inference method as its particular case. The previous full implication inference principles are improved, and unified forms of the new method are respectively established for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) to let different fuzzy implications be used under the same way. Furthermore, reversibility properties of the new method are analyzed from some conditions that many fuzzy implications satisfy, and it is found that its reversibility properties seem fine. Lastly, the more general α-symmetric implicational method is put forward, and its unified forms are achieved.     

模糊推理三Ⅰ算法的还原性

模糊推理算法的还原性是判断蕴涵算子与推理方法配合效果的一个重要标准,只有蕴涵算子与推理方法搭配适当,才能使模糊推理有一个好的效果。本文对模糊推理三I算法具备还原性的条件进行了研究。首先,当与蕴涵算子相伴随的三角模为连续三角模时,给出了FM P问题三I算法具有还原性的充要条件;其次,当蕴涵算子为连续的正则蕴涵算子时,给出了FM T问题的三I算法具有还原性的充要条件;最后,当正则蕴涵算子关于补运算满足对合律时,给出了FM T问题三I算法满足还原性的一个充分条件。     

粗糙模糊集与模糊粗糙集的截集性质

研究粗糙模糊集、模糊粗糙集、广义粗糙模糊集和广义模糊粗糙集的截集性质,并且还研究了基于逻辑算子的广义模糊粗糙集的基本性质。     

The influence of some fuzzy implication operators on the accuracy of a fuzzy model-Part I

The problem of the influence of fuzzy implication operators and connective also on the accuracy of a fuzzy model of a d.c. series motor is considered. Several typical fuzzy implication operators are used to construct the fuzzy model of a d.c. series motor. A root-mean-square error is adopted as the criterion of the model's adequacy to the real system. The best typical fuzzy relations are selected.     

Modeling holistic fuzzy implication using co-copulas

Two related aggregation operators called copulas and co-copulas are introduced and various properties are described. The relationship, of these operators to t-norms and t-conorms is noted. Generalizations of these, respectively, called conjunctors and disjunctors, are introduced. We suggest the use of disjunctor operators for modeling the multi-valued implication operator in fuzzy logic. We point out that the selection of operators used in fuzzy logic, in addition to having appropriate pointwise properties, should be holistic, this requires consideration of the nature of the resulting fuzzy set as a whole. Focusing on the protoform of fuzzy modus ponens and looking at the information contained in the inferred fuzzy set we show that the use of co-copulas has some desirable properties. Taking advantage of the fact that the weighted sum of co-copulas is a co-copula we consider the problem of constructing customized implication operators.     

Toward extended fuzzy logic—A first step

Fuzzy logic adds to bivalent logic an important capability—a capability to reason precisely with imperfect information. Imperfect information is information which in one or more respects is imprecise, uncertain, incomplete, unreliable, vague or partially true. In fuzzy logic, results of reasoning are expected to be provably valid, or p-valid for short. Extended fuzzy logic adds an equally important capability—a capability to reason imprecisely with imperfect information. This capability comes into play when precise reasoning is infeasible, excessively costly or unneeded. In extended fuzzy logic, p-validity of results is desirable but not required. What is admissible is a mode of reasoning which is fuzzily valid, or f-valid for short. Actually, much of everyday human reasoning is f-valid reasoning.f-Valid reasoning falls within the province of what may be called unprecisiated fuzzy logic, FLu. FLu is the logic which underlies what is referred to as f-geometry. In f-geometry, geometric figures are drawn by hand with a spray pen—a miniaturized spray can. In Euclidean geometry, a crisp concept, C, corresponds to a fuzzy concept, f-C, in f-geometry. f-C is referred to as an f-transform of C, with C serving as the prototype of f-C. f-C may be interpreted as the result of execution of the instructions: Draw C by hand with a spray pen. Thus, in f-geometry we have f-points, f-lines, f-triangles, f-circles, etc. In addition, we have f-transforms of higher-level concepts: f-parallel, f-similar, f-axiom, f-definition, f-theorem, etc. In f-geometry, p-valid reasoning does not apply. Basically, f-geometry may be viewed as an f-transform of Euclidean geometry.What is important to note is that f-valid reasoning based on a realistic model may be more useful than p-valid reasoning based on an unrealistic model.