There are many concepts that are used in fuzzy sets that sometimes become useful when studying fuzzy control. The following problems introduce some of the more popular fuzzy set concepts that not treate were not treated earlier in the chapter. (a)The\support\ of a fuzzy set with membership function (x) is the(crisp) set of all points x on the universe of discourse such

Develop a graphical depiction of the operation of the fuzzy controller for the inverted pendulum similar to 3 π the one given in Figure2.1 99 on page46. For this choose(t)=andet)=, which will result in four rules being on. Be sure to show all parts of the graphical depiction

There are many concepts that are used in fuzzy logic that sometimes become useful when studying fuzzy control. The following problems introduce some of the more popular fuzzy logic oncepts that were not treated earlier in the chapter or were treated only briefly (a)The complement(\not )of a fuzzy set with a membership function has a membership function given by A(x)=1-u(x). Sketch the complement of the fuzzy set shown in Figure 2.6 on page 30 (b)There are other ways to def ine the\triangular norm\for representing

（ 1） 都是非数值型的非线性函数的逼近器、估计器、和动态系统； （2） 不需要数学模型进行描述，但都可用数学工具进行处理； （3）都适合于VLSI、光电器件等硬件实现

模块（组合）网络 （1） 产生的背景 （a) 更好的映射非线性函数 （b) 模拟人类神经系统,分工合作 （c) 在控制中,克服“时间交叉”(Temporal Crosstalk) 现象

（1）精确逻辑（传统逻辑）的一些概念 命题逻辑、布尔代数、和集合论是同构的。 隐含是重要的概念。 传统的命题逻辑中，命题的“真”和“假”必须具有 意义。逻辑推理是给定一个命题，组合成另一个命题的过 程

模糊系统辨识的问题分类 1、静态系统的辨识，它包括： （1）参数辨识 （2）结构辨识 2、动态系统的辨识 （1）结构辨识 （2）系统行为的辨识

一、模糊逻辑控制器的基本结构 二、模糊控制系统的设计 三、PID 控制器模糊增益调节 四、模糊系统的稳定性分析 五、利用MATLAB设计模糊控制器

竞争学习和Kohonen自组织网络 竞争学习根据输入模式来更新权值，输入单元i与所有输 出单元j 用wij 连接。输入的数目即为输入的维数，输出的 数目即为输入数据要聚类的数目

原理：从小脑活动只获取启发 （1）小脑从各种传感器获得信号、反馈和命令，构成地址，地址的内容形成各种所需的动作。 （2）输出的动作只限制在最活跃神经中的一个小子集，绝大多数神经元都受到抑制