模糊逻辑

Fuzzy Logic

Logic, according to Webster's dictionary, is the science of the normative formal principles of reasoning. In this sense, fuzzy logics concerned with the formal principles of approximate reasoning, with precise reasoning viewed as a limiting case.

In more specific terms, what is central about fuzzy logic is that, unlike classical logical systems, it aims at modeling the imprecise modes of reasoning that play an essential role in the remarkable human ability to make rational decisions in an environment of uncertainty and imprecision. This ability depends, in turn, on our ability to infer an approximate answer to a question based on a store of knowledge that is inexact, incomplete, or not totally reliable. For example:

(1) Usually it takes about an hour to drive from Berkeley to Stanford about half an hour to drive form Stanford to San Jose. How long would it take to drive from Berkeley to San Jose via Stanford?

(2)Most of those who live in Belvedere have high incomes. It is probable that Mary lives in Belvedere. What can be said about Mary's income?

(3)Slimness is attractive. Carol is slim. Is Carol attractive?

(4)Brian is much taller than most of his close friends. How tall is Brian?

There are two main reasons why classical logical systems cannot cope with problems of this type. First, they do not provide a system for representing the meaning of propositions expressed in a natural language when the meaning is imprecise; and second, in those cases in which ten meaning can be represented symbolically in a meaning representation language, for example, a semantic network or a conceptual-dependency graph, there is no mechanism for inference.

As will be seen, fuzzy logic addresses these problems in the following ways. First, the meaning of a lexically imprecise proposition is represented as an elastic constraint on a variable; and second, the answer to a query is deduced through a propagation of elastic constraints.

During the past several years, fuzzy logic has found numerous applications in fields ranging from finance to earthquake engineering. But what is striking is that its most

important and visible application today is in a realm not anticipated when fuzzy logic was conceived, namely, the realm of fuzzy-logic-based process control. The basic idea underlying fuzzy logic control was suggested in notes published in 1968 and 1972 and described in greater detail in 1973. The first implementation was pioneered by Mamdani and Asslian in 1974 in connection with the regulation of a steam engine. In the ensuing years, once the basic idea underlying fuzzy logic control because well understood, many applications followed. In japan, in particular, the use of fuzzy logic in control processes is being pursued in many application areas, among them automatic train operation, vehicle control, robot control, speech recognition, and stabilization control. More about some of these projects will be said in the section dealing with applications.

In most of the current applications of fuzzy logic, software is employed as a medium for the implementation ,of fuzzy algorithms and control rules. What is clear, however, is that it would be cheaper and more effective to use fuzzy logic chips and , eventually, fuzzy computers. The first logic chip was developed by Togai and Watanabe at Bell Telephone Laboratories in 1985, and it is likely to become available for commercial us in 1988 or 1989. On the heels of this important development came the announcement of a fuzzy computer designed by Yamakawa at Kumamoto University. These developments on the hardware front may lead to an expanded use of fuzzy logic not only in industrial application but, more generally, in knowledge-based systems in which the deduction of an answer to a query requires the inference machinery of fuzzy logic.

One important branch of fuzzy logic may be called dispositional logic. This logic, as its name implies, deals with dispositions, that is propositions that are preponderantly but not necessarily always true. For example, "snow is white" is a disposition, as are the propositions "swedes are blond" and " high quality is expensive." a disposition may be viewed as a usuality-qualified proposition in which the qualifying quantifier "usually" is implicit rather than explicit. In this sense, the disposition " snow is white" may be viewed as the result of suppressing the fuzzy quantifier "usually" in the usuality-qualified proposition.

In this proposition, "usually" plays the role of a fuzzy proportion of the form shown in Figure 1.

The importance of dispositional logic stems from he fact that most of what is usually referred to as common sense knowledge may be viewed as a collection of dispositions. Thus, the main concern of dispositional logic lies in the development of rules inference from common sense knowledge.

In what follows, i present a condensed exposition of some basic ideas underlying fuzzy logic and describe some representative applications. More detailed information regarding fuzzy logic and its applications may be found in te cited literature.

Fuzzy logic is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi-channel PC or workstation-based data acquisition and control systems. It can be implemented in hardware, software, or a combination of both. Fuzzy logic provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. Fuzzy logic's approach to control problems mimics how a person would make decisions, only much faster.

Fuzzy logic requires some numerical parameters in order to operate such as what is considered significant error and significant rate-of-change-of-error, but exact values of these numbers are usually not critical unless very responsive performance is required in which case empirical tuning world determine them. For example, a simple temperature control system could use a single temperature feedback sensor whose data is substracted from the command signal to compute "error" and then time-differentiated to yield the error slope or rate-of-change-error, hereafter called "error-dot". Error might have units of degs F and a small error considered to be 2F while a large error is 5F

模糊逻辑

根据韦氏词典，逻辑是指对规范形式原理推理的科学。从这意义上说，模糊逻辑与形式原理的近似原理相关，把精确推理市委一种极限情况。

用更具体的术语来表达的话，与经典逻辑系统不同，模糊逻辑的重点在于，它的目标在于建立不精确推理模式。而这个模式在人类在一个不确定和不精确的环境下做出理性决定能力中有着重要的作用。反过来说，这种能力取决于我们基于不准确、不完整或不完全可靠的储备知识的前提下来推断一个近似答案的能力。例如：

（1）一般来说，从伯克利开车到斯坦福需要大约一个小时，从斯坦福到圣何塞需要大概半个小时。那么，从圣何塞开车到伯克利，通过斯

坦福需要多少时间呢？

（2）大多是住在奔来菲德尔的人都有高收入。玛丽也可能就住在那，那么，我们能说一下关于玛丽收入的问题吗？

（3）苗条的人比较吸引人。卡罗很苗条，她有魅力吗？

（4）布莱恩比他的好朋友们高很多，他有多高呢？

经典逻辑系统无法解决这种类型问题的原因有两个。第一，当词意表达不明确的时候，它不提供一个系统表示自然语言表达的命题意义。第二，这些例子中的情况是十个含义可以象征性地用一个意义的表现语言来代表。例如，一个语义网络或者一个概念依赖图。这些是没有推理机制的。

我们可以看到，模糊逻辑用以下各种方法阐释了这些问题。首先，词汇方面意义不精确的命题都被表示为一个弹性约束的不断变量。第二，问卷答案的推导是通过弹性约束的传播来查询的。

在过去的几年中，模糊逻辑在各种领域的应用被不断挖掘，从金融到地震工程。但引人注目的是，它在今日最重要和最普遍的应用不是模糊逻辑构思预期，而是基于模糊逻辑的过程领域控制。最基础的模糊逻辑控制概念基础据说是在1968和1972年发表与笔记中的，1973年才详细描述。第一个实现连接与调节蒸汽引擎最早是在1974年由阿斯利安和曼达尼完成。在接下来的几年中，因为关于模糊逻辑控制所隐含的基本概念充分被理解，重新挖掘出更多的应用程序。特别是在日本，控制流中模糊逻辑的使用在很多应用领域总正在不断地赶上世界水

平，特别是自动车操控、车辆控制、机器人控制、语音识别和稳定性控制。更多关于这些项目的信息将在处理应用程序部分细说。

当前，大多数的模糊逻辑应用中，都使用软件为媒介，以实现模糊算法和控制规格。然而，更为清楚的是，使用模糊逻辑芯片乃至最终的模糊计算机才是最模糊逻辑最便宜也是最有效的使用。第一个逻辑芯片是有佟盖和渡边于1985年在贝尔电话实验室发明的。而且它在1988或1989年称为商业化可供给。紧跟在这一重要发展的面世，亚麻卡瓦在熊本大学又设计出一个模糊计算机。这些硬件前的发展可能会使模糊逻辑的应用范围大幅度增加，不仅仅是在工业领域，更为普遍的是在知识库系统中，一个问卷答案的查询需要模糊逻辑推理机械。

模糊逻辑一个重要的分支可以称为外在逻辑。顾名思义，外在逻辑专门处理一些不用一定总是争取的外在命题。例如，“雪是白色的”是一种惯性思维，就像“瑞典人都是金发碧眼的”和“高质量的东西都是昂贵的”。一个斯文可能被视为一个常理命题，就像“通常“是隐式的而不是显式的。在这个意义上，命题“雪是白色的”可能被视为模糊量词抑制的结果。

在这个命题中，“通常”发挥的作用是一个模糊比例，就像图1所示的表单。

外在逻辑的重要性源于它的大部分事实通常都被称为常识，可能被看做一个命题的集合。因此，外在逻辑的主要关注在于从常识推理规则的发展。

接下来，我讲介绍一些浓缩的基本理论，特别是关于模糊逻辑的一些隐义。同时，我也会细说一些具有代表性的应用程序。更多关于模糊逻辑及其应用程序的信息可能会再引用文献中出现.

模糊逻辑控制系统是一个解决问题的方法，有助于实现系统从简单的、小的、嵌入式调试到大型的、网络化的、多通道的数据采集和pc或基于工作站的控制系统，它可以实现软件、硬件或两者的结合。模糊逻辑提供了一个简单的方法来得出一个明确的结论。虽然这个结论是基于含糊其辞、模棱两可的、不精确的、喧闹的或残缺的信息。模糊逻辑控制的解决方法是更快地模拟一个人如何做出决定。

模糊逻辑需要一些数值参数来操作，如被认为什么都很重要的误差和显著的误差变化率。但这些确切值数字通常都不是关键，除非在这种情况下灵敏性能是十分急需的。他们的经验优化确定世界。路人，一个简单的温度控制系统可以通

过一个单一的温度反馈传感器的数据分散，从命令信号来计算“误差”，然后时间分化产生误差的斜率或变化速度误差，一下成为“误差点“。误差的单位为F，而一个I额小错位是2F，大型错误则是5F。