人工智能课程模糊逻辑.ppt

模糊逻辑与模糊推理 Motivation 一提到数学，人们自然会想到它是精确的(set)。然而精确数学却不能有效描述现实世界里普遍存在的模糊想象，如“好与坏”，“长与短”、“一大堆”，“一小撮”，“太冷”，“太热”，“物美价廉”，这些“量”在人们的头脑都有一个人们普遍接受的标准，利用这些模糊量非但没有影响人们的信息交流，反倒能便于理解与记忆。 模糊逻辑是一种精确解决不精确、不完全信息的方法。模糊逻辑可以比较自然地处理人的概念，它是一种通过模仿人的思维方式来表示和分析不确定、不精确信息的方法和工具. 模糊逻辑，不同于经典逻辑在真和假之间没有精确的边界，即从真到假之间的转变是逐渐，这个过程通过隶属度函数来描述。 模糊并非来源于集合组成元素的随机性，而是来源于抽象思维和概念的不确定性及不精确本质。 History The precision of mathematics（精确数学） owes its success in large part to the efforts of Aristotle（亚里斯多德）。 Their efforts led to a concise theory of logic and mathematics. The “Law of the Excluded Middle”（排除中间） states that every proposition must either be True or False. Plato反对这种非此即彼的思维方法，他认为在真与假之间应该存在一种介于真与假之间的灰色地带的第三区域。 There were strong and immediate objections（缺陷）. For example, Heraclitus（赫拉 克利特）proposed that things could be simultaneously True and not True. History 一百多年前，罗素曾经指出过二元逻辑的局限性。 Lukasiewicz(波兰科学家，卢卡谢维奇 ) 对亚里斯多德的二值逻辑进行改进。提出了多值逻辑。 In the early 1900’s, Lukasiewicz described a three-valued logic. The third value can be translated as the term “possible,” and he assigned it a numeric value between True and False. Later, he explored four-valued logics, five-valued logics, and declared that in principle there was nothing to prevent the derivation of an infinite-valued logic. History Knuth(高德纳) proposed a three-valued logic similar to Lukasiewicz’s.（卢卡谢维奇） He speculated(推测) that mathematics would become even more elegant than in traditional bi-valued logic. His insight was to use the integral range(区间) [-1, 0 +1] rather than [0, 1, 2]. History Lotfi Zadeh（扎德 ）, at the University of California at Berkeley, first presented fuzzy logic in the mid-1960s. Zadeh developed fuzzy logic as a way of processing data. Instead of requiring a data element to be either a member or non-member of a set, he introduced the idea of partial set membership.(他首次提出fuzzy logical，引入部分属于的思想) 1965年发表关于模糊集合理论的论文。 1966年马里诺斯（Marinos）发表关于模糊逻辑的研究报告。 以后，扎德（L.A.Zadeh）又提出关于模糊语言变量的概念。 1974年扎德（L.A.Zadeh）进行有关模糊逻辑推理的研究。 扎德的重要贡献在于将模糊和数学统