模糊信息处理北京大学 谭营 智能信息处理PPT课件

1、1普通集合u集合的概念集合的概念第1页/共48页2普通集合 集合的表示方法第2页/共48页3普通集合 集合的并、交、差、补第3页/共48页4 集合运算规则第4页/共48页5对应关系第5页/共48页6特征函数第6页/共48页7 特征函数的运算 集合的特征函数表示第7页/共48页8集合的直积第8页/共48页9关系矩阵第9页/共48页10第10页/共48页11Let A be a setDefine a function, called characteristic function , A: X 0, 1AxifAxifxA10)(ExampleA = set of all even number

2、A(2) = 1A(3) = 0Crisp sets第11页/共48页12Fuzzy setsA: X 0, 1The tree height is 22 m.24024,22()90045sin(221)22,20105 . 0200)(xiftifxtiftifxxifxA第12页/共48页13模糊集第13页/共48页14第14页/共48页15模糊集例子第15页/共48页16模糊集合 第16页/共48页17模糊性与随机性 模糊性总是伴随着复杂性而出现。 复杂性意味着因素的多样性、关联的多样性 随机性：事件是否发生的因果律被破坏而造成的一种不确定性。 模糊性：事物本身性态和属性的不确定性。从

3、信息观点看：随机性只涉及信息的量，模糊性关系到信息的意义、信息的定性问题。模糊性是一种比随机性更深刻的不确定性。第17页/共48页18模糊集合的表示-Zadeh表示法第18页/共48页19模糊集合的表示-向量表示法第19页/共48页20模糊集合的表示-隶属函数表示法第20页/共48页21隶属函数的确定 1、Fuzzy统计法第21页/共48页22怎样确定隶属函数？1. Subjective evaluation and elicitation As fuzzy sets are usually intended to model peoples cognitive states, they ca

4、n be determined from either simple or sophisticated elicitation procedures. At they very least, subjects simply draw or otherwise specify different membership curves appropriate to a given problem. These subjects are typically experts in the problem area. Or they are given a more constrained set of

5、possible curves from which they choose. Under more complex methods, users can be tested using psychological methods. 2. Ad-hoc forms While there is a vast (hugely infinite) array of possible membership function forms, most actual fuzzy control operations draw from a very small set of different curve

6、s, for example simple forms of fuzzy numbers. This simplifies the problem, for example to choosing just the central value and the slope on either side. 第22页/共48页233. Converted frequencies or probabilities Sometimes information taken in the form of frequency histograms or other probability curves are

7、 used as the basis to construct a membership function. There are a variety of possible conversion methods, each with its own mathematical and methodological strengths and weaknesses. However, it should always be remembered that membership functions are NOT (necessarily) probabilities. 4. Physical me

8、asurement Many applications of fuzzy logic use physical measurement, but almost none measure the membership grade directly. Instead, a membership function is provided by another method, and then the individual membership grades of data are calculated from it. 5. Learning and adaptation 第23页/共48页24隶属

9、函数的确定 2、几种常见的隶属函数形式第24页/共48页25常见的隶属函数形式第25页/共48页26第26页/共48页27模糊集合的基本运算第27页/共48页28第28页/共48页29例子第29页/共48页30模糊集合运算的基本规则第30页/共48页31第31页/共48页32第32页/共48页33模糊关系 定义：第33页/共48页34第34页/共48页35模糊关系矩阵和关系图第35页/共48页36第36页/共48页37截矩阵第37页/共48页38截矩阵的性质第38页/共48页39模糊关系的运算第39页/共48页40例子第40页/共48页41第41页/共48页42模糊关系的性质第42页/共48页43模糊逻辑-模糊语言 第43页/共48页44语言变量的表征第44页/共48页45模糊推理第45页/共48