模糊信息處理-北京大學(xué) 譚營 智能信息處理

1、1智能信息處理智能信息處理課程課程第二講第二講 模糊信息處理技術(shù)模糊信息處理技術(shù)主講：主講： 譚譚 營營 教授教授北京大學(xué)信息科學(xué)技術(shù)學(xué)院智能科學(xué)系北京大學(xué)信息科學(xué)技術(shù)學(xué)院智能科學(xué)系2007年9月14日（星期五3、4節(jié),二教421）2普通集合普通集合u集合的概念集合的概念3普通集合普通集合u集合的表示方法集合的表示方法4普通集合普通集合u集合的并、交、差、補集合的并、交、差、補5u集合運算規(guī)則集合運算規(guī)則6對應(yīng)關(guān)系對應(yīng)關(guān)系7特征函數(shù)特征函數(shù)8u特征函數(shù)的運算特征函數(shù)的運算u集合的特征函數(shù)表示集合的特征函數(shù)表示9集合的直積集合的直積10關(guān)系矩陣關(guān)系矩陣1112Let A be a setDefi

2、ne a function, called characteristic function , A: X 0, 1AxifAxifxA10)(ExampleA = set of all even numberA(2) = 1A(3) = 0Crisp sets13Fuzzy setsA: X 0, 1The tree height is 22 m.24024,22()90045sin(221)22,20105 . 0200)(xiftifxtiftifxxifxA14模糊集模糊集1516模糊集例子模糊集例子17模糊集合模糊集合u 18模糊性與隨機性模糊性與隨機性u模糊性總是伴隨著復(fù)雜性而出現(xiàn)。

3、模糊性總是伴隨著復(fù)雜性而出現(xiàn)。u復(fù)雜性意味著因素的多樣性、關(guān)聯(lián)的多樣性復(fù)雜性意味著因素的多樣性、關(guān)聯(lián)的多樣性u隨機性：事件是否發(fā)生的因果律被破壞而造隨機性：事件是否發(fā)生的因果律被破壞而造成的一種不確定性。成的一種不確定性。u模糊性：事物本身性態(tài)和屬性的不確定性。模糊性：事物本身性態(tài)和屬性的不確定性。從信息觀點看：隨機性只涉及信息的量，模糊性關(guān)系到信息的意義、信息的定性問題。模糊性是一種比隨機性更深刻的不確定性。19模糊集合的表示模糊集合的表示-Zadeh表示法表示法20模糊集合的表示模糊集合的表示-向量表示法向量表示法21模糊集合的表示模糊集合的表示-隸屬函數(shù)表示法隸屬函數(shù)表示法22隸屬函數(shù)的

4、確定隸屬函數(shù)的確定u1、Fuzzy統(tǒng)計法統(tǒng)計法23怎樣確定隸屬函數(shù)？u1. Subjective evaluation and elicitation As fuzzy sets are As fuzzy sets are usually intended to model peoples cognitive states, they usually intended to model peoples cognitive states, they can be determined from either simple or sophisticated can be determined fr

5、om either simple or sophisticated elicitation procedures. At they very least, subjects simply elicitation procedures. At they very least, subjects simply draw or otherwise specify different membership curves draw or otherwise specify different membership curves appropriate to a given problem. These

6、subjects are appropriate to a given problem. These subjects are typically experts in the problem area. Or they are given a typically experts in the problem area. Or they are given a more constrained set of possible curves from which they more constrained set of possible curves from which they choose

7、. Under more complex methods, users can be choose. Under more complex methods, users can be tested using psychological methods. tested using psychological methods. u2. Ad-hoc forms While there is a vast (hugely infinite) While there is a vast (hugely infinite) array of possible membership function f

8、orms, most actual array of possible membership function forms, most actual fuzzy control operations draw from a very small set of fuzzy control operations draw from a very small set of different curves, for example simple forms of fuzzy different curves, for example simple forms of fuzzy numbers. Th

9、is simplifies the problem, for example to numbers. This simplifies the problem, for example to choosing just the central value and the slope on either choosing just the central value and the slope on either side.side. 24u3. Converted frequencies or probabilities Sometimes Sometimes information taken

10、 in the form of frequency histograms information taken in the form of frequency histograms or other probability curves are used as the basis to or other probability curves are used as the basis to construct a membership function. There are a variety of construct a membership function. There are a va

11、riety of possible conversion methods, each with its own possible conversion methods, each with its own mathematical and methodological strengths and mathematical and methodological strengths and weaknesses. However, it should always be weaknesses. However, it should always be remembered that members

12、hip functions are NOT remembered that membership functions are NOT (necessarily) probabilities. (necessarily) probabilities. u4. Physical measurement Many applications of fuzzy Many applications of fuzzy logic use physical measurement, but almost none logic use physical measurement, but almost none

13、measure the membership grade directly. Instead, a measure the membership grade directly. Instead, a membership function is provided by another method, membership function is provided by another method, and then the individual membership grades of data are and then the individual membership grades of data are calculated from it. calculated from it. u5. Learning and adaptation 25隸屬函數(shù)的確定隸屬函數(shù)的確定u2、幾種常見的隸屬函數(shù)形式、幾種常見的隸屬函數(shù)形式26常見的隸屬函數(shù)形式常見的隸屬函數(shù)形式2728模糊集合的基本運算模糊集合的基本運算2930例子例子31模糊集合運算的基本規(guī)則模糊集合運算的基本規(guī)則323334模糊關(guān)系模糊關(guān)系u定義：定義：3536模糊關(guān)系矩陣和關(guān)系圖模糊關(guān)系矩陣和關(guān)系圖3738截