What Is Fuzzy Logic?

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1 Getting Started 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 long history of use in AI, what is missing in such systems is a mechanism for dealing with fuzzy consequents and fuzzy antecedents. In fuzzy logic, this mechanisms provided by 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 (FDCL). Although FDCL is not used explicitly in the toolbox, it is effectively one of its principal constituents. In most of the applications of fuzzy logic, a fuzzy logic solution is, in reality, a translation of a human solution into FDCL. A trend 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, hard computing, soft computing accommodates the 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 the future, soft computing could 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. 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 neuro-fuzzy systems. 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 toolbox. Fuzzy logic is all about the relative importance of precision: How important is it to be exactly right when a rough answer will do? You can use Fuzzy Logic Toolbox software with MATLAB technical computing software as 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. 1-6
What Is Fuzzy Logic? In this sense, fuzzy logic is both old and new because, although the modern and methodical science of fuzzy logic is still young, the concepts of fuzzy logic relies on age-old skills of human reasoning. Precision and Significance in the Real World A 1500 kg mass is approaching your head at 45.3 m/s LOOK OUT!! Precision Significance Fuzzy logic is a convenient way to map an input space to an output space. Mapping input to output is the starting point for everything. Consider the following examples: • With information about how good your service was at a restaurant, a fuzzy logic system can tell you what the tip should be. • With your specification of how hot you want the water, a fuzzy logic system can adjust the faucet valve to the right setting. • With information about how far away the subject of your photograph is, a fuzzy logic system can focus the lens for you. • With information about how fast the car is going and how hard the motor is working, a fuzzy logic system can shift gears for you. Agraphical example of an input-output map is shown in the following figure. 1-7
Page 1 and 2: Fuzzy Logic Toolbox 2 User’s Guid
Page 3: Revision History January 1995 First
Page 6 and 7: Overview of Fuzzy Inference Process
Page 8 and 9: Simulink Environment ..............
Page 10 and 11: x Contents
Page 12 and 13: 1 Getting Started Product Overview
Page 14 and 15: 1 Getting Started If you just want
Page 18 and 19: 1 Getting Started Input Space (all
Page 20 and 21: 1 Getting Started do a fine job wit
Page 22 and 23: 1 Getting Started An Introductory E
Page 24 and 25: 1 Getting Started See how the formu
Page 26 and 27: 1 Getting Started tip=(0.15)*servRa
Page 28 and 29: 1 Getting Started 0.25 0.2 tip 0.15
Page 30 and 31: 1 Getting Started or perhaps rewrit
Page 32 and 33: 2 Tutorial Overview The point of fu
Page 34 and 35: 2 Tutorial Foundations of Fuzzy Log
Page 36 and 37: 2 Tutorial How does it work? Reason
Page 38 and 39: 2 Tutorial One of the most commonly
Page 40 and 41: 2 Tutorial A fuzzy set is an extens
Page 42 and 43: 2 Tutorial Polynomial based curves
Page 44 and 45: 2 Tutorial A B min(A,B) A B max(A,B
Page 46 and 47: 2 Tutorial the fuzzy sets to be com
Page 48 and 49: 2 Tutorial if temperature is cold t
Page 50 and 51: 2 Tutorial Fuzzy Inference Systems
Page 52 and 53: 2 Tutorial Information flows from l
Page 54 and 55: 2 Tutorial selects the maximum of t
Page 56 and 57: 2 Tutorial In the following diagram
Page 58 and 59: 2 Tutorial 1. if and then Interpret
Page 60 and 61: 2 Tutorial Customization Oneofthepr
Page 62 and 63: 2 Tutorial adaptive neural fuzzy in
Page 64 and 65: 2 Tutorial Getting Started We’ll
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2 Tutorial Name of the system. Chan
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2 Tutorial 8 Select File > Export >
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2 Tutorial Editor shares some featu
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2 Tutorial can first use the mouse
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2 Tutorial d Verify that 3 is selec
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2 Tutorial 5 In the FIS Variables a
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2 Tutorial Now that the variables h
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2 Tutorial one of the variable qual
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2 Tutorial A literal interpretation
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2 Tutorial Notice that under food,
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2 Tutorial Upon opening the Surface
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2 Tutorial Building Fuzzy Inference
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2 Tutorial Specifying Custom Member
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2 Tutorial 3 In the FIS Editor, sel
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2 Tutorial Using the custmf1 exampl
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2 Tutorial 6 To add custom membersh
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2 Tutorial In the toolbox, the AND
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2 Tutorial 1 In the lower-left pane
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2 Tutorial Working from the Command
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2 Tutorial The structure.field synt
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2 Tutorial After closing any open M
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2 Tutorial 25 20 tip 15 10 5 10 8 6
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2 Tutorial a.output(1).mf(2).type='
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2 Tutorial All the information for
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2 Tutorial 44. 2 The list of comman
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2 Tutorial Working in Simulink Envi
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2 Tutorial 2 1.8 1.6 1.4 1.2 1 0.8
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2 Tutorial 0.8 0.6 0.4 0.2 valve 0
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2 Tutorial If you stop the simulati
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2 Tutorial FIS. This automatic mode
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2 Tutorial Type slcp attheMATLABpro
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2 Tutorial As the figure shows, the
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2 Tutorial The final output of the
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2 Tutorial the Sugeno-type represen
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2 Tutorial and the membership funct
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2 Tutorial anfis and the ANFIS Edit
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2 Tutorial alone or in combination
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2 Tutorial Constraints of anfis anf
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2 Tutorial You can also load Testin
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2 Tutorial Validating the Trained F
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2 Tutorial The training data appear
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2 Tutorial 1 Choose Grid partition,
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2 Tutorial Viewing Your FIS Structu
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2 Tutorial The plot shows the check
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2 Tutorial • Select the Checking
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2 Tutorial In this case, the checki
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2 Tutorial anfis from the Command L
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2 Tutorial data values. You use the
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2 Tutorial subplot(2,2,4) plotmf(fi
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2 Tutorial Thedifferencebetweentheo
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2 Tutorial As a result, the trainin
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2 Tutorial Output FIS Structure for
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2 Tutorial Output FIS Structure for
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2 Tutorial right location within a
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2 Tutorial Here, the variable cente
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2 Tutorial Finally, plot the two cl
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2 Tutorial The genfis2 function bui
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2 Tutorial fismat=genfis2(datin,dat
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2 Tutorial At this point, you can u
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2 Tutorial The next figure shows th
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2 Tutorial you fit the fuzzy system
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2 Tutorial Plot the checking error
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2 Tutorial information on the clust
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2 Tutorial Saving the Cluster Cente
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2 Tutorial The fis.c file contains
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2 Tutorial This command saves the i
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2 Tutorial 'lcclnk' is not recogniz
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2 Tutorial 7 To verify that the fuz
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3 Function Reference GUI Tools and
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3 Function Reference FIS Data Struc
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3 Function Reference Simulink Envir
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addmf Purpose Syntax Description Ad
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addrule Purpose Syntax Description
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anfis Purpose Syntax Description Tr
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anfis training data set. When you s
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anfisedit Purpose Syntax Descriptio
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defuzz Purpose Syntax Description D
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dsigmf See Also gaussmf, gauss2mf,
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evalfis • ORR: the result of eval
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fcm Purpose Syntax Description Fuzz
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findcluster Purpose Syntax Descript
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fuzarith Purpose Syntax Description
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fuzzy Purpose Syntax Open basic Fuz
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fuzzy Membership functions to invok
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gauss2mf See Also dsigmf, gauss2mf,
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gbellmf Purpose Syntax Description
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genfis1 The default number of membe
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genfis2 Purpose Syntax Description
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genfis2 Xin1 = 7*rand(50,1); Xin2 =
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genfis2 Example 3 The following exa
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genfis3 The input membership functi
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genfis3 Example 3 The following exa
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gensurf Example 1 a = readfis('tipp
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getfis 'inlabels' 'outlabels' 'inra
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getfis getfis(a,'input',1) Name = s
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mam2sug Purpose Syntax Description
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mf2mf 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
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mfedit Selecttheiconforthevariableo
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newfis DefuzzMethod ans = [newsys]
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pimf Purpose Syntax Description Exa
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plotmf Purpose Syntax Description E
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psigmf Purpose Syntax Description B
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mmf Purpose Syntax Description Remo
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mvar Purpose Syntax Description Rem
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uleedit Purpose Syntax Description
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uleview Purpose Syntax Rule viewer
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setfis Purpose Syntax Description S
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sffis Purpose Syntax Description Fu
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showfis 24. average 25. generous 26
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showrule 1. (service==poor) | (food
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sigmf See Also dsigmf, gaussmf, gau
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subclust Purpose Syntax Description
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subclust Examples [C,S] = subclust(
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surfview If you want to create a sm
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trapmf Purpose Syntax Description T
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trimf Purpose Syntax Description Tr
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writefis Purpose Syntax Description
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zmf See Also dsigmf, gaussmf, gauss
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5 Block Reference Controllers Fuzzy
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5 Block Reference Membership Functi
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Diff. Sigmoidal MF Purpose Descript
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Fuzzy Logic Controller with Rulevie
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Gaussian2 MF Purpose Description Co
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Pi-shaped MF Purpose Description Se
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Probabilistic Rule Agg Purpose Desc
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S-shaped MF Purpose Description See
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Trapezoidal MF Purpose Description
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Z-shaped MF Purpose Description See
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A Examples Introductory Examples
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B Bibliography [1] Bezdec, J.C., Pa
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B Bibliography [22] Zadeh, L.A.,
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Glossary fuzzy c-means clustering A
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Glossary Glossary-4
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Index H hybrid method 2-121 I if-th
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What Is Fuzzy Logic?

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