模糊信息处理-北京大学谭营智能信息处理选读.ppt

信息科学技术概论 《智能信息处理》课程 第二讲 模糊信息处理技术 主讲： 谭 营 教授 北京大学信息科学技术学院智能科学系 普通集合 普通集合 集合的表示方法 普通集合 集合的并、交、差、补 集合运算规则 对应关系 特征函数 集合的直积 关系矩阵 模糊集 模糊集例子 模糊集合 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。 模糊集合的表示----Zadeh表示法 模糊集合的表示----向量表示法 模糊集合的表示----隶属函数表示法 隶属函数的确定 1、Fuzzy统计法 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 can 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 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 curves, 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. 3. Converted frequencies or probabilities Sometimes information taken in the form of frequency histograms or other probability curves are 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 measurement 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 隶属函数的确定 2、几种常见的隶属函数形式 常见的隶属函数形式 模糊集合的基本运算 例子 模糊集合运算的基本规则 模糊关系 定义： 模糊关