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Fuzzy Logic Toolbo
x™ 2
User’s Guide
How to Contact MathWorks
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com
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The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098
For contact information about worldwide offices, see the MathWorks Web site.
Fuzzy Logic Toolbox™ User’s Guide
© COPYRIGHT 1995–2011 The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or cop ied only under the terms of the license agreement. No part of this manual may be photocopied or
reproduced in any form without prior written consent from Th e MathWorks, Inc.
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation
by, for, or through the federal government of the United States. By accepting delivery of the Program
or Documentatio n, the gov ernment hereby agrees that this software or documentation qualifies as
commercial computer software or commercial computer software documentation as such terms are used
or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the term s and
conditions of this Agreement and on ly those rights specified in thi s Agr eement, shall pertain to and govern
theuse,modification,reproduction,release,performance,display,anddisclosureoftheProgramand
Documentation by the federal governm ent (or other entity ac quiring fo r or t hrough the federal government)
and shall supersede any conflicting contractual terms or conditions. If this License fails to meet the
government’s needs or is inconsistent in any respect w ith federal procurement law, the government agrees
to return the Program and Documentation, unused, to The MathWorks, Inc.
Trademarks
MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See
www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand
names may be trademarks or registered trademarks of their respective holders.
Patents
MathWorks products are protected by one or more U.S. patents. Please see
www.mathworks.com/patents for more information.
Revision History
January 1995 First printing
April 1997 Second printing
January 1998 Third printing
September 2000 Fourth printing Revised for Version 2 (Release 12)
April 2003 Fifth printing
June 2004 Online only Updated for Version 2.1.3 (Release 14)
March 2005 Online only Updated for Version 2.2.1 (Release 14SP2)
September 2005 Online only Updated for Version 2.2.2 (Release 14SP3)
March 2006 Online only Updated for V ersion 2.2.3 (Release 2006a)
September 2006 Online only Updated for V ersion 2.2.4 (Release 2006b)
March 2007 Online only Updated for V ersion 2.2.5 (Release 2007a)
September 2007 Online only Revised for Version 2.2.6 (Release 2007b)
March 2008 Online only Revised for Version 2.2.7 (Release 2008a)
October 2008 Online only Revised for Version 2.2.8 (Release 2008b)
March 2009 Online only Revised for Version 2.2.9 (Release 2009a)
September 2009 Online only Revised for Version 2.2.10 (Release 2009b)
March 2010 Online only Revised for Version 2.2.11 (Release 2010a)
September 2010 Online only Revised for Version 2.2.12 (Release 2010b)
April 2011 Online only Revised for Version 2.2.13 (Release 2011a)
Contents
Getting Started
1
Product Overview ................................. 1-2
Fuzzy Logic Toolbox Description
..................... 1-2
Installation
...................................... 1-2
Using This Guide
................................. 1-3
What Is Fuzzy Logic?
............................... 1-4
Description of Fuzzy Logic
.......................... 1-4
Why Use Fuzzy Logic?
............................. 1-7
When Not to Use Fuzzy Logic
....................... 1-8
What Can Fuzzy Logic Toolbox Software Do?
........... 1-9
An Introductory Example: Fuzzy Versus Nonfuzz y
Logic
........................................... 1-11
The Basic Tipping Problem
......................... 1-11
The Nonfuzzy Approach
............................ 1-11
The Fuzzy Logic Approach
.......................... 1-15
Problem Solution
.................................. 1-16
Tutorial
2
Overview ......................................... 2-2
Foundations of Fuzzy Logic
........................ 2-4
Fuzzy Sets
....................................... 2-4
Membership Functions
............................. 2-8
Logical O perations
................................ 2-13
If-Then Rules
..................................... 2-16
Fuzzy Inference Systems
........................... 2-20
v
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