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.     

基于解析结构的模糊控制器的稳定性和一致逼近性分析

基于模糊控制的解析结构理论,设计了输入变量采用三角形、全交迭,等差间距分布的隶属函数,输出变量采用对称、均匀分布的单点隶属函数和线性控制规则的二维模糊控制器,推导了模糊控制器的解析表达式。利用Lyapunov第二法论证了该模糊控制系统在平衡点处的局部稳定性,并证明了模糊控制器的一致逼近性。     

模糊规则在线自调整算法及仿真研究*

在模糊规则的可修正因子的基础上,提出了一种在线自调整模糊控制器解析规则模糊控制器的改进结构,引入了能够动态调整模糊控制规则的修正函数;同时,通过遗传算法,应用该修正函数对模糊控制器控制参数进行优化。通过对一个典型的二阶系统进行仿真实验,结果表明使用该方法设计的模糊控制器具有响应快、超调小、稳态精度高等优点,改善了模糊控制系统的性能。     

基于解析结构的模糊控制器的设计

一般常规模糊器设计中，隶属函数采用对称均匀分布曲线，此方法存在一定的不足，采用Sum-Product推理方法，等比间距不均匀分布隶属函数的模糊控制器，在控制性能上优于常规模糊控制器，可提高系统的快速性和鲁棒性，同时大大减少了隶属函数中需优化参数的个数，在解析结构理论研究的基础上对所设计的模糊控制器进行了定性和定量的分析，分析结果和仿真实验证明了该方法的优真性和有效性。     

采用非线性规则和不均匀分布的输入输出隶属函数时典型模糊控制器的结构分析

针对两输入 (e,Δe)一输出 (Δu)的典型模糊控制器, 其输入变量采用三角形、全交迭、对称、不均匀分布的隶属函数, 输出变量采用对称、不均匀分布的单点隶属函数, 当采用非线性控制规则和Sum Product推理方法时, 推导了输出的解析表达式, 分析了其结构特性和极限特性, 证明了此类模糊控制器具有通用逼近性, 并讨论了典型模糊控制系统的局部稳定性.     

一类模糊系统的逼近问题

对于一类模糊系统，首次给出了它们可在紧论域上以任意要求的精度逼近任意C^1函数的构造性充分条件，同时导出了可用于计算所需模糊规则条数的显式公式，对于多项式函数情形，证明了所给结果比献[1]中结果保守性要小。     

基于广义模糊基函数的多变量模糊模型及其辨识方法

利用模糊穴位映射理论，提出一种有效描述复杂多变量系统的模糊模型－－广义模糊基函数展开式，它可方便地处理多输入多输出系统的语言和系统信息，并可逼近任意非线性函数，是一种通用的多变量模糊逻辑系统模型。利用语言信息，提出一种新的自适应参数辨识方法－－改进的Ｗｉｄｒｏｗ－Ｈｏｆｆ学习规则，仿真结果验证了它的有效性。     

基于规则插入的自适应模糊控制器的设计

提出一种为模糊控制器系统开发有效规则的自适应模糊控制器的设计方法.该方法首先基于两个基本的If-then模糊规则,然后插入多个新If_then模糊规则,其合成的模糊规则的输入_输出映射保持不变,且其隶属函数的参数在线约束为最小化成本函数,最后以最典型的非线性和延迟系统模型为例进行仿真实验,结果证明了该设计方法的有效性.     

一种模糊CMAC神经网络

提出了一种模糊CMAC(小脑模型关节控制器)神经网络,它由输入层、模糊化层、模糊相 联层、模糊后相联层与输出层等5层节点组成,具有与CMAC相似的单层连接权,可通过BP 算法学习推论参数或模糊规则.给出了网络的连接结构与学习算法,并将其应用于函数逼近 问题中仿真结果验证了该方法较之CMAC的优越性.     

正则模糊神经网络是模糊值函数的泛逼近器

通过分析多元模糊值Bernstein多项式的近似特性，证明了4层前向正则模糊神经网络（FNN）的逼近性能，该类网络构成了模糊值函数的一类泛逼近器，即在欧氏空间的任何紧集上，任意连续模糊值函数能被这类FNN逼近到任意精度，最后通过实例给出了实现这种近似的具体步骤。     

On fuzzy equality and approximation in fuzzy logic

The paper is a contribution to the theory of fuzzy logic in narrow sense with evaluated syntax (FLn). We show that the concepts of fuzzy equality and the provability degree enable to generalize the concept of fuzzy approximation. In the second part of the paper we return to the Mamdani-Assilian formula, which is formed on the basis of the so called totally bounded fuzzy equality and using which we can approximate any function with the prescribed accuracy.This paper has been supported by Grant A1187901/99 of the GA AV R and the project VS96037 of MMT of the Czech Republic.     

Constructions of fuzzy functions based on fuzzy equalities

 The strong (perfect) fuzzy function have been applied to approximate reasoning and vague algebra in the literature of fuzzy sets. The construction of strong (perfect) fuzzy functions possesses an important role for their applications. In the presented paper, some of the results on the construction of strong (perfect) fuzzy functions are improved, and several new and desirable results in this direction are obtained. Furthermore, it is also shown that how these results can be used to point out the connections between fuzzy functions in the classical sense and the strong (perfect) fuzzy functions.     

Fuzzy failure modes and effects analysis by using fuzzy TOPSIS-based fuzzy AHP

Failure mode and effects analysis (FMEA) is a widely used engineering technique for designing, identifying and eliminating known and/or potential failures, problems, errors and so on from system, design, process, and/or service before they reach the customer (Stamatis, 1995). In a typical FMEA, for each failure modes, three risk factors; severity (S), occurrence (O), and detectability (D) are evaluated and a risk priority number (RPN) is obtained by multiplying these factors. There are significant efforts which have been made in FMEA literature to overcome the shortcomings of the crisp RPN calculation. In this study a fuzzy approach, allowing experts to use linguistic variables for determining S, O, and D, is considered for FMEA by applying fuzzy ‘technique for order preference by similarity to ideal solution’ (TOPSIS) integrated with fuzzy ‘analytical hierarchy process’ (AHP). The hypothetical case study demonstrated the applicability of the model in FMEA under fuzzy environment.     

模糊决策的基础——模糊集比较与排序

研究模糊决策中模糊集的比较与排序问题。通过引入模糊极大集和模糊极小集为参照系统并以海明距离为计量工具，定义了两个模糊效用函数和一个模糊优先关系作为模糊集的排序指标。前者适合于多个模糊集的整体分析，后者适合于两两之间的比较判别。对于两个模糊集的排序问题，模糊效用函数自动退化为相应的模糊优先关系。系统分析了3种指标的性能及关系，并举例说明了它们的应用。     

Data-driven fuzzy modeling for Takagi-Sugeno-Kang fuzzy system

This paper presents a systematic approach to design first order Tagaki-Sugeno-Kang (TSK) fuzzy systems. This approach attempts to obtain the fuzzy rules without any assumption about the structure of the data. The structure identification and parameter optimization steps in this approach are carried out automatically, and are capable of finding the optimal number of the rules with an acceptable accuracy. Starting with an initial structure, the system first tries to improve the structure and, then, as soon as an improved structure is found, it fine tunes its rules’ parameters. Then, it goes back to improve the structure again to find a better structure and re-fine tune the rules’ parameters. This loop continues until a satisfactory solution (TSK model) is found. The proposed approach has successfully been applied to well-known benchmark datasets and real-world problems. The obtained results are compared with those obtained with other methods from the literature. Experimental studies demonstrate that the predicted properties have a good agreement with the measured data by using the elicited fuzzy model with a small number of rules. Finally, as a case study, the proposed approach is applied to the desulfurization process of a real steel industry. Comparing the proposed approach with some other fuzzy systems and neural networks, it is shown that the developed TSK fuzzy system exhibits better results with higher accuracy and smaller size of architecture.     

Technical importance ratings in fuzzy QFD by integrating fuzzy normalization and fuzzy weighted average

Fuzzy quality function deployment (QFD) has been extensively used for translating customer requirements (CRs) into product design requirements (DRs) in fuzzy environments. Existing approaches, however, for rating technical importance of DRs in fuzzy environments are found problematic, either incorrect or inappropriate. This paper investigates how the technical importance of DRs can be correctly rated in fuzzy environments. A pair of nonlinear programming models and two equivalent pairs of linear programming models are developed, respectively, to rate the technical importance of DRs. The developed models are examined and illustrated with two numerical examples.     

A fuzzy neural network with fuzzy impact grades

Fuzzy rule derivation is often difficult and time-consuming, and requires expert knowledge. This creates a common bottleneck in fuzzy system design. In order to solve this problem, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a fuzzy neural network based on mutual subsethood (MSBFNN) and its fuzzy rule identification algorithms. In our approach, fuzzy rules are described by different fuzzy sets. For each fuzzy set representing a fuzzy rule, the universe of discourse is defined as the summation of weighted membership grades of input linguistic terms that associate with the given fuzzy rule. In this manner, MSBFNN fully considers the contribution of input variables to the joint firing strength of fuzzy rules. Afterwards, the proposed fuzzy neural network quantifies the impacts of fuzzy rules on the consequent parts by fuzzy connections based on mutual subsethood. Furthermore, to enhance the knowledge representation and interpretation of the rules, a linear transformation from consequent parts to output is incorporated into MSBFNN so that higher accuracy can be achieved. In the parameter identification phase, the backpropagation algorithm is employed, and proper linear transformation is also determined dynamically. To demonstrate the capability of the MSBFNN, simulations in different areas including classification, regression and time series prediction are conducted. The proposed MSBFNN shows encouraging performance when benchmarked against other models.     

The equivalence between fuzzy Mealy and fuzzy Moore machines

We study the relationships between fuzzy Mealy and fuzzy Moore machines in the frame of truth values in a lattice-ordered monoid. In particular, we show that lattice-valued sequential-like machines and lattice-valued finite Moore machines are equivalent in the sense they exhibit the same input–output characteristics.     

Multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques

In this paper, we present a new method for multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques. First, the proposed method constructs training samples based on the variation rates of the training data set and then uses the training samples to construct fuzzy rules by making use of the fuzzy C-means clustering algorithm, where each fuzzy rule corresponds to a given cluster. Then, we determine the weight of each fuzzy rule with respect to the input observations and use such weights to determine the predicted output, based on the multiple fuzzy rules interpolation scheme. We apply the proposed method to the temperature prediction problem and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) data. The experimental results show that the proposed method produces better forecasting results than several existing methods.     

Generating fuzzy rules from training instances for fuzzy classification systems

In recent years, many methods have been proposed to generate fuzzy rules from training instances for handling the Iris data classification problem. In this paper, we present a new method to generate fuzzy rules from training instances for dealing with the Iris data classification problem based on the attribute threshold value α, the classification threshold value β and the level threshold value γ, where α  [0, 1], β  [0, 1] and γ  [0, 1]. The proposed method gets a higher average classification accuracy rate than the existing methods.