模糊逻辑工具箱

1、Glossary 术语表Adaptive Neuro-Fuzzy Inference System(ANFIS) A technique for automatically tuning Sugeno-type inference systems based on training data.Foreword （前言）The past few years have witnessed a rapid growth in the number and variety of applications of fuzzy logic. The applications range from consu

2、mer products such as cameras, camcorders, washing machines, and microwave ovens to industrial process control, medical instrumentation, decision-support systems, and portfolio selection.过去几年间， 模糊逻辑无论是在应用数量上还是应用种类上都呈现快速增长的趋势。 其应用 范围从消费产品，例如照相机， 便携式摄像机， 洗衣机，及微波炉到工业过程控制，医药器 具，决策支持系统，以及部长职务选举等To underst

3、and the reasons for the growing use of fuzzy logic it is necessary, first, to clarify what is meant by fuzzy logic. 为了理解模糊逻辑为何能得以如此快速使用，首先，有必要理清什么是模糊逻辑。Fuzzy logic has two different meanings. In a narrow sense, fuzzy logic is a logical system, which is an extension of multivalued logic. But in a wid

4、er sense, which is in predominant use today, fuzzy logic (FL) is almost synonymous with the theory of fuzzy sets, a theory which relates to classes of objects with unsharp boundaries in which membership is a matter of degree. In this perspective, fuzzy logic in its narrow sense is a branch of FL. Wh

5、at is important to recognize is that, even in its narrow sense, the agenda of fuzzy logic is very different both in spirit andsubstance from the agendas of traditional multivalued logical systems. 模糊逻辑有两种含义。 从狭义上来说， 模糊逻辑是一个逻辑系统， 它是一种多值逻辑的扩充。 但是广义上来说，就今天多数使用情况来看，模糊逻辑（FL ）几乎与模糊理论的同义，这里模糊理论是一种与事物无明显界限的

6、的分类， 点，狭义上说，模糊逻辑应该是模糊逻辑理论（ 楚模糊逻辑与以往传统的多值逻辑系统无论是在 也不相同。在这个界限里关系是一个度的问题。 以此观FL）的一个分支。重要的是，我们要认清 精神还是主旨上都不相同， 甚至从狭义角度In the Fuzzy Logic Toolbox, fuzzy logic should be interpreted as FL, that is, fuzzy logic in its wide sense. The basic ideas underlying FL are explained very clearly and insightfully in

7、theIntroduction. What might be added is that the basic concept underlying FL is that of a linguistic variable, that is, a variable whose values are words rather than numbers. In effect, much of FL may be viewed as a methodology for computing with words rather than numbers. Although words are inheren

8、tly less precise than numbers, their use is closer to human intuition. Furthermore, computing with words exploits the tolerance for imprecision and thereby lowers the cost of solution.在模糊逻辑工具箱，模糊逻辑应该理解为 FL,即模糊逻辑的广义定义。在介绍中，FL的潜 在的 基本的意义已经解释的非常清楚和明白。这里，需要增加说明的是， FL 潜在的基本含 义是一种关于语言上的变量， 也就是说， 一种既有数字又有语

9、句的变量。 事实上，绝大多数，FL 在计算机处理中作为方式逻辑通常被视为语句而不是数字。尽管在精度上，语句与生俱 来就比数字低， 但是其使用更接近人类的直觉认识。 另外，语句的计算处理开拓了 imprecision 的容度，因此也减小了解决费用。Another basic concept in FL, which plays a central role in most of its applications, is that of a fuzzy if-then rule or, simply, fuzzy rule. Although rule-based systems have a l

10、ong history of use in AI, what is missing in such systems is a machinery for dealing with fuzzy consequents and/or fuzzy antecedents. In fuzzy logic, this machinery is provided by what is called the calculus of fuzzy rules. The calculus of fuzzy rules serves as a basis for what might be called the F

11、uzzy Dependency and Command Language (FDCL). Although FDCL is not used explicitly in the Fuzzy Logic Toolbox, it is effectively one of its principal constituents. In this connection, what is important to recognize is that in most of the applications of fuzzy logic, a fuzzy logic solution is in reali

12、ty a translation of a human solution into FDCL.FL 另外一种基础概念就是模糊 if-then 规则，或者更简单地说，是一种模糊规则，此种情况 用的比较多，也扮演了一个中心角色。尽管基于规则的系统用在 AI 中有很长一段历史，但 是，此类系统缺少一个能处理模糊结果与/或者是模糊先例的机器。在模糊逻辑中，这种机器可以由一种被称为模糊规则的计算所提供。 模糊规则计算为模糊独立与命令语言 (FDCL ) 提供了基础。尽管， FDCL 在模糊逻辑工具箱中不能明确地使用，但是作为原则成分相当有 效。在连接中，重要的是，认清模糊逻辑的绝大多数应用，事实上，模糊

13、逻辑的解决方案是 一种转换为 FDCL 的人类解决方式。What makes the Fuzzy Logic Toolbox so powerful is the fact that most of human reasoning and concept formation is linked to the use of fuzzy rules. By providing a systematic framework for computing with fuzzy rules, the Fuzzy Logic Toolbox greatly amplifies the power of hu

14、man reasoning. Further amplification results from the use of MATLAB and graphical user interfaces, areas in which The MathWorks has unparalleled expertise.3 大部分人类缘由与概念形成与模糊规则的使用相关联使得模糊逻辑工具箱如此之强大。 为计 算处理模糊规则而提供了一种系统性的架构，模糊逻辑工具箱大大地增强了人类理由的力 量。从 matlab 及图形用户界面的使用， 更深一步增强化的结果， 可以从 MathWorks 中获得。 A trend

15、 that is growing in visibility relates to the use of fuzzy logic in combination with neurocomputing and genetic algorithms. More generally, fuzzy logic, neurocomputing, and genetic algorithms may be viewed as the principal constituents of what might be called soft computing. Unlike the traditional,

16、hard computing, soft computing is aimed at an accommodation with the pervasive imprecision of the real world. The guiding principle of soft computing is: Exploit the tolerance for imprecision, uncertainty, and partial truth to achieve tractability, robustness, and low solution cost. In coming years,

17、 soft computing is likely to play an increasingly important role in the conception and design of systems whose MIQ (Machine IQ) is much higher than that of systems designed by conventional methods. 有一种趋势是模糊逻辑与神经计算及遗传算法的结合使用。 更一般地， 模糊逻辑， 神经元计 算及遗传算法可以被视为原则成分， 一种被称为软计算的成分。 不像传统的硬计算， 软计算 的目标是实现与现实世界的普遍

18、深入的映射。软计算的指导性原则是:开拓映射的容度，不确定性，及部分真实性然后获得易处理性、鲁棒性及较低的解决费用。在接下来的几年里， 在 MIQ 比习惯性方式设计的系统高的多，软计算可能扮演越来越重要的角色。Among various combinations of methodologies in soft computing, the one that has highest visibility at this juncture is that of fuzzy logic and neurocomputing, leading to so-called neuro-fuzzy syst

19、ems. Within fuzzy logic, such systems play a particularly important role in the induction of rules from observations. An effective method developed by Dr. Roger Jang for this purpose is called ANFIS (Adaptive Neuro-Fuzzy Inference System). This method is an important component of the Fuzzy Logic Too

20、lbox.在软计算各式各样的逻辑方式结合中， 在此结合点， 最显著的是模糊逻辑及神经元计算导致 所谓的神经模糊系统。 在模糊逻辑中 ，这种系统扮演了一个非常重要的角色带观测器的规则。 Roger 博士专为此目的发明了一种有效的方法。此方法叫做 ANFIS (应用神经模糊内部系 统)。这种方式是模糊逻辑工具箱的重要组件。The Fuzzy Logic Toolbox is highly impressive in all respects. It makes fuzzy logic an effective tool for the conception and design of intell

21、igent systems. The Fuzzy Logic Toolbox is easy to master and convenient to use. And last, but not least important, it provides a reader-friendly and up-to-date introduction to the methodology of fuzzy logic and its wide-ranging applications. 模糊逻辑工具箱在各方面都令人印象深刻。 对智能系统的设计及其概念来说， 模糊逻辑是一 种有效的工具。 模糊逻辑工具箱

22、容易掌握并且方便使用。 最后，最重要的是， 提供了一种用 户友好和对模糊逻辑方式及时更新的说明以及广泛的应用。Lotfi A. Zadeh Berkeley, CA January 10, 1995Getting StartedWhat Is Fuzzy Logic? Fuzzy logic is all about the relative importance of precision 什么是模糊逻辑？ 模糊逻辑是关于精确度的相对重要性。What Is the Fuzzy Logic Toolbox?The Fuzzy Logic Toolbox is a collection of fu

23、nctions built on the MA TLAB? numeric computing environment. It provides tools for you to create and edit fuzzy inference systems within the framework of MATLAB, or if you prefer, you can integrate your fuzzy systems into simulations with Simulink?. You can even build stand-alone C programs that cal

24、l on fuzzy systems you build with MATLAB. This toolbox relies heavily on graphical user interface (GUI) tools to help you accomplish your work, although you can work entirely from the command line if you prefer. 模糊逻辑工具箱是一系列基于 matlab 运行环境的函数集合。工具箱里可以供你在 matlab 框 架中创建及编辑模糊推论系统，或者如果你愿意，你可以把你的模糊系统集成到 si

25、mulink 仿真中。甚至你可以建立单独的 C 语言的模糊系统来替代用 MATLAB 语言创建的。 这个工 具箱非常依赖图形用户界面( GUI )，以此来帮助你完成工作，尽管你喜欢完全在命令行里 工作。The toolbox provides three categories of tools: 工具箱提供了三种工具： Comma nd line fun ctio ns命令行函数 Graphical in teractive tools图形交互工具 Simulink blocks and examples simulink 模块与例子The first category of tools is

26、 made up of functions that you can call from the command line or from your own applications. Many of these functions are MA TLAB M-files, series of MA TLAB statements that implement specialized fuzzy logic algorithms. You can view the MATLAB codefor these functions using the statement 第一类工具由函数构成，这些函

27、数你可以从命令行或从你自己的应用中调用。这些函数中 有 MA TLAB 的 M 文件，也有一系列执行特定模糊逻辑算法的MATLAB 描述。你可以查看使用这些陈述的的函数的 MATLAB 代码。type function_name 类型 函数名称 You can change the way any toolbox function works by copying and renaming the M-file, then modifying your copy. You can also extend the toolbox by adding your own M-files.Second

28、ly, the toolbox provides a number of interactive tools that let you access many of the functions through a GUI. Together, the GUI- based tools provide an environment for fuzzy inference system design, analysis, and implementation.The third category of tools is a set of blocks for use with the Simuli

29、nk simulation software. These are specifically designed for high speed fuzzy logic inference in the Simulink environment.你可以通过复制或者是重命名 M 文件来改变任何工具箱中函数的工作路径。你也可以通过 增加你自己的 M 文件来扩展工具箱。其次，工具箱提供了许多交互工具，这些工具能让你 通过 GUI 进入许多函数。总之，基于 GUI 的工具箱为模糊推论系统的设计、分析及执行提 供了一个环境。 第三类工具是一系列与 simulink 仿真软件结合使用的模块。 这些模块是专门

30、为 simulink 环境下高速模糊逻辑推论而设计的。Installation 安装To install this toolbox on a workstation, large machine, or a PC, see the installation documentation for that platform.为了在工作站， 大型机械， 及个人计算机上安装此工具箱， 请参看与此平台相关的安装文件。 To determine if the Fuzzy Logic Toolbox is already installed on your system, check for a subdi

31、rectory named fuzzy within the main toolbox directory or folder. 为确保模糊逻辑工具箱已在你的系统中安装，请检查在主工具箱目录中是否有一个名为 fuzzy 的子目录。Using This Guide 使用指南If you are new to fuzzy logic, begin with . This introduces the motivation behind fuzzy logic and leads you smoothly into the tutorial.如果你是初次接触模糊逻辑， 开始，这里介绍了模糊逻辑背后的

32、动机及引导你顺利进入指南。 If you are an experienced fuzzy logic user, you may want to start at the beginning of Tutorial to make sure you are comfortable with the fuzzy logic terminology in the Fuzzy Logic Toolbox. If you just want an overview of each graphical tool and examples of specific fuzzy system tasks,

33、turn directly to Building Systems with the Fuzzy Logic Toolbox . This section does not include information on the adaptive data modeling application covered by the toolbox function ANFIS. The basic functionality of this tool can be found in the section entitled The ANFIS Editor GUI. 如果你已经是一个富有经验的模糊逻

34、辑用户， 为确保你对模糊逻辑工具箱里模糊逻辑术语的 舒适度， 你可能会喜欢从指南开头的地方开始。 如果你仅仅想对每一个图形工具及特定模糊 系统任务有一个大致的浏览， 那么请直接转向模糊逻辑工具想中的创建系统。 此区域不包括那些被工具箱函数ANFIS覆盖的关于适应性数据模型应用的信息。此工具基本函数性质可以在ANFIS编辑器GUI中找到。If you just want to start as soon as possible and experiment, you can open an example system right away by typing如果你想尽快的开始及实验，你可以通过

35、查看类型立刻打开一个例子。fuzzy tipper模糊小费This displays the Fuzzy Inference System (FIS) editor for an example decision making problem that has to do with how to tip in a restaura nt.此例演示了一个关于如何在餐馆处理小费问题的决策的例子，为此而建立的模糊推论系统。All toolbox users should use Functions Alphabetical List for information on specific tools

36、 or functions. Refere nee descripti ons in clude a syn opsis of the functions syn tax, as well as a complete expla nati on of opti ons and operati on. Many reference descriptio ns also in clude helpful examples, a description of the functions algorithm, and references to additional reading material.

37、 For GUI-based tools, the descriptions include options for invoking the tool.所有工具箱用户必须使用到关于特定工具或者函数的函数字母列表。参考描述包括函数构造的大纲，以及一个完整的选择和操作的解释。许多参考描述同样也包括一些有用的例子，函数算法的描述，以及附加阅读材料的参考文献。对基于GUI的工具，这里的描述包括对调用工具的选择。What Is Fuzzy Logic?Fuzzy logic is all about the relative importanee of precision: How important

38、 is it to be exactly right whe n a rough an swer will do? All books on fuzzy logic begi n with a few good quotes on this very topic, and this is no excepti on. Here is what some clever people have said in the past.模糊逻辑是关于精确度的相对重要性：当有一个粗略描述的答案时， 精确的，正确的到底有多么重要？所有关于模糊逻辑的书籍都是以关于此问题的引言为开始的，无一例外。以下是一些名人以

39、前对此问题的见解。Precisi on is not truth. Henri Matisse精确度不是事实。一亨利马迪沙Sometimes the more measurable drives out the most important. Ren Dubos有时，测量越多，越能揪出问题的最重要的部分。一里纳都波斯Vague ness is no more to be done away with in the world of logic tha n frictio n in mecha nics.Charles San ders PeirceI believe that no thi n

40、g is uncon diti on ally true, and hence I am opposed to every stateme nt of positive truth and every man who makes it. H. L. Men cke nSo far as the laws of mathematics refer to reality, they are not certain. And so far as they are certa in, they do not refer to reality. Albert Ein ste inAs complexit

41、y rises, precise stateme nts lose meaning and meanin gful stateme nts lose precisi on. Lotfi ZadehSome pearls of folk wisdom also echo these thoughts.一些明间谚语也能反映这些思想Dont lose sight of the forest for the trees. 不以一叶而障目。Dont be penny wise and pound foolish.The Fuzzy Logic Toolbox for use with MATLAB is

42、 a tool for solvi ng problems with fuzzy logic.Fuzzy logic is a fascinating area of research because it does a good job of trading off between sig ni fica nee and precisi on someth ing that huma ns have bee n man agi ng for a very long time.MATLAB模糊逻辑工具箱是一个用来解决模糊逻辑的工具。模糊逻辑是一个令人惊奇的研 究领域，因为它在重要性及精确度两者

43、之间要取舍的非常好一一一些人类长期希望得以解决 的问题。Fuzzy logic sometimes appears exotic or intimidating to those unfamiliar with it, but once you become acqua in ted with it, it seems almost surpris ing that no one attempted it soon er. I n this sense fuzzy logic is both old and new because, although the moder n and metho

44、dical scie nee of fuzzy logic is still young, the concepts of fuzzy logic reach right down to our bones.对那些不熟悉模糊逻辑的人来说，模糊逻辑有时显得很陌生，使人胆怯，但是你一旦掌握了它，它却看起来不是那么惊奇以至于没有人不想立刻尝试。在此意义上，模糊逻辑是既老又新，因为尽管模糊逻辑的现代系统的科学理论还不是很成熟，但模糊逻辑研究的概念早已深入我们的骨髓。Predsion and Significance In the Re超I WorldA1kg ma 舲Ie approaching yu

45、ur IJ dL 45.3 rifaSignificancePrecisionFuzzy logic is a convenient way to map an in put space to an output space. This is the start ing point for everyth ing else, and the great emphasis here is on the word convenien t.模糊逻辑是一种输入空间到输出空间的方便方式的图形。这里是对其他任何东西的开始点， 这里最需要强调的单词的是“方便”。What do I mean by mapp

46、ing in put space to output space? Here are a few examples: You tell me how good your service was at a restaura nt, and ni tell you what the tip should be. You tell me how hot you want the water, and Ill adjust the faucet valve to the right setting. You tell me how far away the subject of your photog

47、raph is, and ni focus the lens for you. You tell me how fast the car is going and how hard the motor is work ing, and ni shift the gears for you.这里标出输入空间到输出空间是什么意思呢？这里给出一些例子：你告诉我在餐馆的服务质量，然后我告诉你你应该支付的小费。你告诉我你想要多热的水，然后我去调节faucet值到合适的设置点。你告诉我你照片里的物体相隔多远，然后我会为你集中调节长度。你告诉我汽车现在有多快以及发动机的工作难度，然后我会为你调整换挡。A g

48、raphical example of an in put-output map is show n below.下面给出了一个输入输出图形的图形例子。Input SpaceOutput Space他11 possible service(all possible tipsquality ratings)An input-output map for the tipping problem:“Given the quality of service, how much should I tip?Its all just a matter of mapp ing in puts to the a

49、ppropriate outputs. Betwee n the in put and the output well put a black box that does the work. What could go in the black box? Any nu mber of thin gs: fuzzy systems, li near systems, expert systems, n eural n etworks, differe ntial equati ons, in terpolated multidimensional lookup tables, or even a

50、 spiritual advisor, just to name a few of the possible optio ns. Clearly the list could go on and on.这是关于由输入得到合适的输出量的问题。在输入与输出之间，我们放入一个能起作用的黑箱子。怎样处理这个黑箱子呢？此类事情有：模糊系统、线性系统、专家系统、神经网络、 微分方程、interpolated multidimensional lookup tables、甚至是一个精神建议者，去命名一些 可能的选择。很明显地，这个单子可以越来越多。Of the doze ns of ways to make

51、 the black box work, it turns out that fuzzy is ofte n the very best way. Why should that be? As Lotfi Zadeh, who is con sidered to be the father of fuzzy logic, once remarked: I n almost every case you can build the same product without fuzzy logic, but fuzzy is faster and cheaper.在能使黑箱子工作的这么多方式中，结

52、果证明模糊经常是最好的方式。为什么如此呢？正如被视为模糊逻辑之父的 Lotfi Zadeh曾说：“在几乎所有的案例中， 你都可以建立同样的产品， 而此产品并无模糊逻辑，但是如果用模糊逻辑建立的话能更快更便宜。”Why Use Fuzzy Logic?Here is a list of gen eral observati ons about fuzzy logic:以下是对模糊逻辑的一般性观察 Fuzzy logic is con ceptually easy to un dersta nd.在概念上，模糊逻辑容易理解。The mathematical con cepts beh ind fu

53、zzy reas oning are very simple. What makes fuzzy nice is the n atura In ess of its approach and not its far-reach ing complexity.模糊缘由背后的数学概念是非常简单的。 模糊接近的自然属性及 它的远程的简单性 使得模糊 很好。 Fuzzy logic is flexible.模糊逻辑非常灵活With any given system, its easy to massage it or layer more functionality on top of it with

54、out starting again from scratch.对于任何给定的系统， 无需从它的结构入手， 就可以很容易掌握它的信息或者是在它之上的 更多函数特性。 Fuzzy logic is tolerant of imprecise data.模糊逻辑是非精确数据的容度。Everything is imprecise if you look closely enough, but more than that, most things are imprecise even on careful inspection. Fuzzy reasoning builds this underst

55、anding into the process rather than tacking it onto the end.如果你观察够仔细的话， 任何事物都是不精确的， 甚至是经过仔细的检查之后， 大多数事物 还是不精确的。模糊缘由把这种理解建立在过程中而不是结果。 Fuzzy logic can model nonlinear functions of arbitrary complexity. 模糊逻辑能够模拟非线性复杂函数。You can create a fuzzy system to match any set of input-output data. This process is

56、 made particularly easy by adaptive techniques like Adaptive Neuro-Fuzzy Inference Systems (ANFIS), which are available in the Fuzzy Logic Toolbox.你可以创建一个模糊系统去匹配任何输入输出数据。这个过程用适应性技术非常容易建立， 例如用适应性神经模糊推论系统( ANFIS )，这种技术在模糊逻辑工具箱是可用的。 Fuzzy logic can be built on top of the experience of experts. 模糊逻辑能够建立

57、在专家经验上。In direct contrast to neural networks, which take training data and generate opaque, impenetrable models, fuzzy logic lets you rely on the experience of people who already understand your system. 与神经网络这种需实验性数据及一般不透明、 不容易看穿的模型进行直接比较时， 模糊逻辑 能让你依赖人们已经理解你系统的经验基础。 Fuzzy logic can be blended with c

58、onventional control techniques. 模糊逻辑可以与常用的控制技术相结合。Fuzzy systems dont necessarily replace conventional control methods. In many cases fuzzy systems augment them and simplify their implementation.模糊系统没有必要取代常用的控制方式。 在许多情况下， 模糊系统可以增强、 简化它们的执 行。 Fuzzy logic is based on natural language.模糊逻辑基于自然语言。The basis for fuzzy logic is the basis for human communication. This observation underpins many of the other statements about fuzzy logic.模糊逻辑的基础是人类交流的基础。这个观察器巩固了许多关于模糊逻辑的其他描述。The last statement is perhaps the most important one and deserves more discussion. Natu