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The applications range from consumer products such as cameras, camcorders, washing machines, and microwave ovens to industrial process intro, medical instrumentation, decision-support systems, and portfolio selection. To understand the reasons for the growing use of fuzzy logic it is necessary, first, to clarify what is meant by fuzzy logic. Fuzzy logic has two different meanings. In a narrow sense, fuzzy logic is a logical system, which is an extension of multivalent logic.

But in a wider 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 unshorn boundaries in which membership is a matter of degree. In this respective, fuzzy logic in its narrow sense is a branch of FL. What is important to recognize is that, even in its narrow sense, the agenda of fuzzy logic is very different both in spirit and substance from the agendas of traditional multivalent logical systems. 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 the Introduction. 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 ether than numbers. In effect, much of FL may be viewed as a methodology for computing with words rather than numbers. Although words are inherently 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.

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 machinery for dealing with fuzzy consequents and/or fuzzy antecedents. In fuzzy OIC, 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 Fuzzy Dependency and Command Language (FADE). Although FADE is not used explicitly in 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 reality a translation of a human solution into FADE. What makes the Fuzzy Logic Toolbox so powerful is the fact that most of human reasoning and concept formation s 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 human reasoning. Further amplification results from the use of MUTUAL and graphical user interfaces – areas in which The Metaphors has unparalleled expertise.

A trend which is growing in visibility relates to the use of fuzzy logic in combination with importuning and genetic algorithms. More generally, fuzzy logic, importuning, and genetic algorithms may be viewed as the principal constituents of what might be called soft computing. Unlike the traditional, 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, soft computing is likely to play an increasingly important role in the conception and design of systems whose MIX (Machine ‘Q) is much higher than that of systems designed by conventional methods. Among various combinations of methodologies in soft computing, the one which has highest visibility t this Juncture is that of fuzzy logic and importuning, leading to so-called neuron- fuzzy systems. Within fuzzy logic, such systems play a particularly important role in the induction of rules from observations. An effective method developed by Dry.

Roger Gang for this purpose is called NAIFS (Adaptive Neuron-Fuzzy Inference System). This method is an important component of the Fuzzy Logic Toolbox. The Fuzzy Logic Toolbox is highly impressive in all respects. It makes fuzzy logic an effective tool for the conception and design of intelligent 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.

If you are an experienced fuzzy logic user, you may want to start at the beginning of Chapter 2, “Tutorial,” to make sure you are comfortable with the fuzzy logic terminology as used by the Fuzzy Logic Toolbox. If you Just want an overview of each graphical tool and examples of specific fuzzy system tasks, turn directly to the section in Chapter 2 entitled “Building Systems with the Fuzzy Logic Toolbox. ” If you just want to start as soon as possible and experiment, you can open an example system right away by typing fuzzy tipper This brings up the Fuzzy Inference System (IFS) editor for an example problem that as to do with tipping.

If you like you can refer to the one page summary of the fuzzy should use Chapter 3, “Reference,” for information on specific tools. Reference descriptions include a synopsis of the function’s syntax, as well as a complete explanation of options and operation. Many reference descriptions also include helpful examples, a description of the function’s algorithm, and references to additional reading material. For GIG-II-based tools, the descriptions include options for invoking the tool. Installation To install this toolbox on a workstation or a large machine, see the Installation Guide or UNIX.

To install the toolbox on a PC or Macintosh, see the Installation Guide for PC and Macintosh. To determine if the Fuzzy Logic Toolbox is already installed on your system, check for a subdirectory names fuzzy within the main toolbox directory or folder. Typographical Conventions To Indicate This Guide Uses Moonscape type Example Example code To assign the value 5 to A, enter MUTUAL output Moonscape type MUTUAL responds with Function names The coos function finds the cosine of each array element. An array is an ordered collection of information. Press the Return key. Chose the File menu.

New terms Keys Menu names, items, and GUI controls Mathematical expressions Italics Boldface with an initial capital letter Boldface with an initial capital letter This vector represents the polynomial p 4 = XX+XX+3. 1-4 What Is Fuzzy Logic? 1-5 Why Use Fuzzy Logic? 1-6 When Not to Use Fuzzy Logic 1-7 What Can the Fuzzy Logic Toolbox Do? 1-8 1-8 1-12 1-13 An Introductory Example: Fuzzy vs.. Non-Fuzzy The Non-Fuzzy Approach The Fuzzy Approach Some Fuzzy logic is all about the relative importance of precision: How important is it to be exactly right when a rough answer will do?

All books on fuzzy logic begin with a few DOD quotes on this very topic, and this is no exception. Here is what some clever people have said in the past: Precision is not truth. -?Henry Matisse Sometimes the more measurable drives out the most important. -?Rene Dubos Vagueness is no more to be done away with in the world of logic than friction in mechanics. -?Charles Sanders Pierce I believe that nothing is unconditionally true, and hence I am opposed to every statement of positive truth and every man who makes it. Ђ?H. L. Mencken So far as the laws of mathematics refer to reality, they are not certain. And so far as they re certain, they do not refer to reality. -?Albert Einstein As complexity rises, precise statements lose meaning and meaningful statements lose precision. -?Loti Gazed There are also some pearls of folk wisdom that echo these thoughts: Don’t lose sight of the forest for the trees. Don’t be penny wise and pound foolish. The Fuzzy Logic Toolbox for use with MUTUAL is a tool for solving problems with fuzzy logic.

Fuzzy logic is a fascinating area of research because it does a good Job of trading off between significance and precision-?something that humans have been managing for a very long time. Fuzzy logic sometimes appears exotic or intimidating to those unfamiliar with it, but once you become acquainted with it, it seems almost surprising that no one attempted it sooner. In this sense fuzzy logic is both old and new because, 1-2 although the modern and methodical science of fuzzy logic is still young, the concepts of fuzzy logic reach right down to our bones.

Precision and Significance in the Real World LOOK OUT!! Precision Significance 1-3 What Is Fuzzy Logic? Fuzzy logic is a convenient way to map an input space to an output space. This is the starting point for everything else, and the great emphasis here is on the word convenient. ” What do I mean by mapping input space to output space? Here are a few examples: You tell me how good your service was at a restaurant, and I’ll tell you what the tip should be. You tell me how hot you want the water, and I’ll adjust the faucet valve to the right setting.

You tell me how far away the subject of your photograph is, and I’ll focus the lens for you. You tell me how fast the car is going and how hard the motor is working, and I’ll shift the gears for you. A graphical example of an input-output map is shown below. Input Space (all possible service quality ratings) Output Space all possible tips) tonight’s service quality Black Box the “right” tip for tonight An input-output map for the tipping problem: “Given the quality of service, how much should I tip? It’s all Just a matter of mapping inputs to the appropriate outputs. Between the input and the output we’ll put a black box that does the work. What could go in the black box? Any number of things: fuzzy systems, linear systems, expert systems, neural networks, differential equations, interpolated multi-dimensional lookup tables, or monkeys with typewriters Just to name a few of the possible options.