基于POFI方法的模糊系统及其响应性能

用逐点模糊优化推理方法(POFI),详细讨论基于6个常见蕴涵算子的模糊系统及其响应函数.首先分别给出基于POFI方法的这些蕴涵算子的FMP算法中寻求推理后件(或前件)的计算表达式.然后指出基于POFI方法的这6个蕴涵算子模糊控制算法均非插值方法,其模糊控制器均只具有阶跃输出功能,而无函数逼近的泛性.     

两类模糊系统具有插值性的充要条件

当模糊系统具有插值性时,它必具有泛逼近性.因此,由插值性可以分析模糊系统的逼近能力.本文讨论了由“交”和“并”的方式聚合推理规则所生成的两类模糊系统的插值性问题.首先,通过分析由“单点”模糊化方法、CRI(com positional ru le of inference)算法以及“重心法”构造的模糊系统,指出模糊系统是否具有插值性关键取决于模糊蕴含算子的第二个变量为0和1时的表达式或取值.在此基础上,得到两类模糊系统具有插值性的充要条件.最后给出了满足这两个充要条件的一些常用的蕴涵算子.     

基于蕴涵算子族H(p,λ)的三I算法模糊系统

针对蕴涵算子族H(p,λ),给出了FMP问题三I支持算法和α-三I支持算法的计算公式;讨论了基于三I算法的模糊系统及其响应性能,结果表明,蕴涵算子族H(p,λ)的模糊系统只具有阶跃输出能力,不具有函数逼近泛性;揭示了蕴涵算子族H(p,λ)的模糊系统的概率意义,给出了其概率分布,它充当模糊系统的“系统内核”作用.     

基于蕴涵算子族H_((p,λ))的三Ⅰ算法模糊系统

针对蕴涵算子族H(p,λ),给出了FMP问题三Ⅰ支持算法和α-三Ⅰ支持算法的计算公式;讨论了基于三Ⅰ算法的模糊系统及其响应性能,结果表明,蕴涵算子族H(p,λ)的模糊系统只具有阶跃输出能力,不具有函数逼近泛性;揭示了蕴涵算子族H(p,λ)的模糊系统的概率意义,给出了其概率分布,它充当模糊系统的"系统内核"作用。     

基于改进遗传算法的模糊控制器设计

针对模糊控制器的隶属度函数和模糊控制规则的选取及优化缺乏自学习能力与知识采集的手段,以及遗传算法具有自适应、启发式、概率性、迭代式全局收敛的特点,该文章将遗传算法与模糊控制相结合,给出了一种基于改进遗传算法的模糊控制器设计策略.改进算法引入了分裂算子来避免遗传算法在寻优过程中陷入局部最优解,同时对编码方式、选择算子、交叉算子以及变异算子做了相应的调整与改进.并将此改进算法用于优化模糊控制器的隶属度函数与模糊控制规则.仿真结果表明用该改进算法优化后的模糊控制器较用普通遗传算法优化后的模糊控制器具有更好的控制性能.     

两类B样条模糊系统及其应用

能够同时逼近函数及其导函数的模糊系统在应用中具有重要意义.本文利用B样条函数作为推理前件,得到了两类能够同时逼近函数及其导函数的B样条模糊系统.其中第一类B样条模糊系统是插值系统且对函数及其一阶导函数分别具有二阶和一阶逼近精度,第二类B样条模糊系统是拟插值系统且对函数及其一阶、二阶导函数均具有二阶逼近精度.最后,将这两类模糊系统应用到一级倒立摆的稳定控制中,仿真结果表明利用这两类模糊系统设计的控制器是可行的,且具有一定的鲁棒性.     

基于三Ⅰ算法的模糊系统的响应能力

探讨模糊系统的函数逼近能力是模糊系统理论研究的一个重要的课题.本文首次讨论了在两种推理规则情形下由三Ⅰ支持度算法和模糊熵三Ⅰ算法设计的模糊系统的响应能力.针对三Ⅰ支持度算法,分别就正则蕴涵算子和11个具体的模糊蕴涵算子,考察了相应模糊系统的响应能力,讨论了基于模糊熵三Ⅰ算法和三Ⅰ算法设计的模糊系统的响应函数之间的关系....     

广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程

首先,通过引入拟减法算子给出K-积分模定义,并针对广义Mamdani模糊系统实施等距剖分其输入空间. 其次,应用分片线性函数（Piecewise linear function,PLF）的性质构造性地证明了广义Mamdani模糊系统在K-积分模意义下具有泛逼近性,从而将该模糊系统对连续函数空间的逼近能力扩展到一类可积函数类空间上. 最后,通过模拟实例给出该广义Mamdani模糊系统对给定可积函数的泛逼近及实现过程.     

π型隶属函数的典型模糊控制器的解析结构

研究了一种新型的典型模糊控制器,它的输入隶属函数采用π型样条函数,具有二阶逼近特性,而一般典型模糊控制器采用的三角形隶属函数只具有一阶逼近特性,因此研究这种新型的模糊控制器具有重要的意义.文章首先给出了该类典型模糊控制器的定义,推导了它的解析表达式,证明了该类典型模糊控制器可以等效为一个全局的二维继电器和一个局部的非线性PD控制器之和.在此基础上,给出了其极限特性和非线性特性.     

泛模糊逻辑控制器研究

文章在总结模糊逻辑控制器一般结构的基础上,采用泛逻辑算子簇柔化了模糊推理操作,从而提出了一种新型的变结构模糊逻辑控制器———泛模糊逻辑控制器,同时使用具有自适应学习率的模糊神经网络BP算法进行训练,可据不同控制对象来确定合适的控制结构。仿真结果表明,该方法是有效的。     

模糊推理的函数变换观点

基于函数论的立场 ,指出模糊推理过程是一个函数变换过程 ,模糊规则蕴涵了一个从函数空间到函数空间的映射 ,现存的种种模糊推理方法都是对这种映射的估计 ,进而指出插值和回归的方法都适用于这种估计。系统地提出了用回归的方法处理模糊推理的思想 ,并结合线性回归模型进行了示范 ,证明了基于线性回归模型的模糊推理系统 (FIS)同样是一个万能函数逼近器。     

折线模糊神经网络对模糊函数的通用逼近

基于折线模糊数间的模糊算术以及一个新的扩展原理建立了一种新的模糊神经网络模型,证明了当输入为负模糊数时,相应的前向三层折线模糊网络可以作为连续模糊函数的通用逼近器,并给出了此时连续模糊函数所需满足的等价条件,最后给出了一个仿真实例。     

Comparison of necessary conditions for typical Takagi-Sugeno andMamdani fuzzy systems as universal approximators

Both Takagi-Sugeno (TS) and Mamdani fuzzy systems are known to be universal approximators. We investigate whether one type of fuzzy approximators is more economical than the other. The TS fuzzy systems are the typical two-input single-output TS fuzzy systems. We first establish necessary conditions on minimal system configuration of the TS fuzzy systems as function approximators. We show that the number of the input fuzzy sets and fuzzy rules needed by the TS fuzzy systems depend on the number and locations of the extrema of the function to be approximated. The resulting conditions reveal the strength of the TS fuzzy approximators. The drawback, though, is that a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. We then compare these necessary conditions with the ones that we established for the general Mamdani fuzzy systems in our previous papers. Results of the comparison unveil that the minimal system configurations of the TS and Mamdani fuzzy systems are comparable. Finally, we prove that the minimal configuration of the TS fuzzy systems can be reduced and becomes smaller than that of the Mamdani fuzzy systems if nontrapezoidal or nontriangular input fuzzy sets are used. We believe that all the results in present paper hold for the TS fuzzy systems with more than two input variables but the proof seems to be mathematically difficult. Our new findings are valuable in designing more compact fuzzy systems, especially fuzzy controllers and models which are two most popular and successful applications of the fuzzy approximators     

线性T-S模糊系统作为通用逼近器的充分条件

作为模糊系统理论研究和实际应用的基础,对模糊系统通用逼近性的研究已经取得了 很大的进展,但是只有为数不多的文献研究了模糊系统作为通用逼近器的充分条件.提出了线 性T-S模糊系统以任意精度一致逼近紧致集上任意连续实函数的一个充分条件,并给出了数值 示例.该示例表明提出的充分条件明显优于现有的其它结果.     

A novel fuzzy neural network and its approximation capability

The polygonal fuzzy numbers are employed to define a new fuzzy arithmetic. A novel ex-tension principle is also introduced for the increasing function σ:R→R. Thus it is convenient to con-struct a fuzzy neural network model with succinct learning algorithms. Such a system possesses some universal approximation capabilities, that is, the corresponding three layer feedforward fuzzy neural networks can be universal approximators to the continuously increasing fuzzy functions.     

典型T-S模糊系统是通用逼近器

研究的多输入单输出T－S模糊系统采用输入变量的线性函数作为规则后件,称为典型T－S模糊系统,在每个输入变量的模糊子集满足一致性以及隶属函数连续且分段可微的条件下,证明了典型T－S模糊系统是通和逼近器,以此为基础,提出当典型T－S模糊系统采用BP算法进行在线学习时,可以仅调节规则后件的参数,而同时仍然能够确保通用逼所性。     

Approximation capability of fuzzy systems using translations anddilations of one fixed function as membership functions

This paper reports on a related study on approximation theory of fuzzy systems. First, some basic principles are presented to construct membership functions. Then, an approach is proposed to form membership functions by using translations and dilations of one fixed function (called a basis function) which is very similar to that in wavelets analysis. The properties of this type of membership function reflect the advantages of the given approach. Finally, it is proved that fuzzy systems based on such membership functions are universal approximators under certain mild conditions on the basis function. This conclusion expands the family of fuzzy systems which can be universal approximators     

Applicability analysis of fuzzy inference by means of generalizedDempster-Shafer theory

The generalization of Dempster-Shafer (D-S) theory to fuzzy sets provides means for evidential reasoning on basis of fuzzy information. Fuzzy implication operators are used to turn partial fuzzy knowledge about a physical system into an inference engine. Presently there are more than 72 fuzzy implication operators known and investigated, evoking demand for strategies of finding the best performing fuzzy implication operator for the physical system under investigation. In this paper the authors propose such a concept based on generalized D-S theory. A convention to update prior knowledge regarding the applicability of fuzzy implication operators, with respect to fuzzy evidences pertaining to the physical system under consideration, is presented