This book is intended to be an undergraduate introduction to the theory
of fuzzy sets. We envision, sometime in the future, a curriculum in
fuzzy sys- tems theory, which could be in computer /information
sciences, mathematics, engineering or economics (business, finance),
with this book as the starting point. It is not a book for researchers
but a book for beginners where you learn the basics. This course would
be analogous to a pre-calculus course where a student studies algebra,
functions and trigonometry in preparation for more advanced courses.
Chapters 3 through 11 are on fuzzy algebra, fuzzy functions, fuzzy
trigonometry, fuzzy geometry, and solving fuzzy equations. However,
after this course the student doesn't go on to calculus but to more
specialized courses in fuzzy systems theory like fuzzy clustering, fuzzy
pattern recogni- tion, fuzzy database, fuzzy image processing and
computer vision, robotics, intelligent agents, soft computing, fuzzy
rule based systems (control, expert systems), fuzzy decision making,
applications to operations research, fuzzy mathematics, fuzzy systems
modeling, etc. Therefore, very little of most of these topics are
included in this book. There are many new topics included in this book.
Let us point out some of them here: (1) mixed fuzzy logic (Section 3.5);
(2) three methods of solving fuzzy equation/problems (Chapter 5); (3)
solving fuzzy inequalities (Chapter 6); (4) inverse fuzzy functions
(Section 8.5); (5) fuzzy plane geometry (Chap- ter 9); (6) fuzzy
trigonometry (Chapter 10); and (7) fuzzy optimization based on genetic
algorithms (Chapter 16).
