Type-2 Fuzzy Logic Systems Book (Draft)

Jerry M. Mendel (mendel@sipi.usc.edu)
Sat, 30 Jan 1999 21:33:27 +0100 (MET)

<fontfamily><param>Times</param>Dear Fuzzy Logic Colleagues:

We have written a book about type-2 fuzzy logic systems. It describes
some very new ideas that will let you model linguistic uncertainty
(words mean different things to different people; so rules that use
words have linguistic uncertainties, e.g., the location of the center
of the membership function for the term 'some to a moderate amount' can
range over an interval) totally within the framework of fuzzy logic.
Type-2 fuzzy logic provides a measure of dispersion that captures the
effects of rule uncertainties. The type-2 fuzzy logic systems that are
described in our book have two kinds of outputs: (1) a type-1 set-which
we call a "type-reduced set"-that plays the role of a confidence
interval, but for linguistic uncertainties, and (2) a defuzzified
output. When all rule uncertainties disappear, then a type-2 fuzzy
logic system reduces to a type-1 fuzzy logic system.

The title of our book is "An Introduction to Type-2 Fuzzy Logic
Systems." Its table of contents is:=20

1. Introduction

2. Operations on Type-2 Sets

3. Properties of Membership Grades

4. Relations and Compositions

5. Fuzzy Logic Systems=20

6. Examples of Type-2 Fuzzy Logic

Systems

7. Conclusions

=46our appendixes with detailed derivations and proofs

Index

A draft copy of this book is now available as a report. Much more
information about this report, as well as how to order it, can be found
on the web page http://sipi.usc.edu/~mendel/report. If you do not have
access to the Internet and are interested in obtaining this report,
please contact me by e-mail, at:
<underline><color><param>0000,0000,00FF</param>mendel@sipi.usc.edu</color></=
underline>.

Jerry Mendel

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