From Our Editors
The most complete, accessible introduction to fuzzy set
theory.
-- Provides all the necessary background for understanding fuzzy
sets, including the basics of information theory, as well as
classical logical and set theories.
-- Introduces fuzzy sets, fuzzy relations, fuzzy arithmetic and
fuzzy logic.
-- Requires minimal mathematical background. Presents all necessary
mathematics, and uses examples from everyday life.
This book is designed to help anyone understand the basics of
fuzzy sets, whether or not they have a mathematical background. The
book first presents a basic grounding in information theory,
classical logic and set theories. Next, it introduces the basics of
fuzzy sets, distinguishing them from traditional crisp sets, and
introducing the concept of membership function. The distinctions
between classical and fuzzy relations are introduced, as are
representations of fuzzy relations; fuzzy equivalence relations;
fuzzy partial orderings, and related topics. The book introduces
fuzzy arithmetic and fuzzy numbers. It also presents a detailed
int
From the Publisher
This book is designed to help anyone understand the basics of
fuzzy sets, whether or not they have a mathematical background.The
book first presents a basic grounding in information theory,
classical logic and set theories. Next, it introduces the basics of
fuzzy sets, distinguishing them from traditional crisp sets, and
introducing the concept of membership function. The distinctions
between classical and fuzzy relations are introduced, as are
representations of fuzzy relations; fuzzy equivalence relations;
fuzzy partial orderings, and related topics. The book introduces
fuzzy arithmetic and fuzzy numbers. It also presents a detailed
introduction to fuzzy logic, multivalued logics, fuzzy
propositions, quantifiers, linguistic hedges and approximate
reasoning. Several basic and advanced applications for fuzzy set
theory are presented as well.Any non-technical reader interested in
fuzzy sets and fuzzy logic. Also ideal for introductory
level-students, whether they are planning a technical or
non-technical course of study.
From the Jacket
34105-7
From the beginning of modern science until the end of the
nineteenth century, uncertainty was generally viewed as undesirable
in science, but with the emergence of statistical mechanics in the
twentieth century, the unmanageable complexity of mechanical
processes on the molecular level led to the adoption of statistical
principles and principles of probability theory. However, in spite
of its success, probability theory alone is not capable of
capturing uncertainty in all of its manifestations, particularly
when it arises from the vagueness of natural language. Thus, a new
theory arose which treats this aspect of uncertainty: fuzzy set
theory.
Fuzzy Set Theory: Foundations and Applications serves
as a simple introduction to basic elements of fuzzy set theory. The
emphasis is on a conceptual rather than a theoretical presentation
of the material. Fuzzy Set Theory also contains an
overview of the corresponding elements of classical set
theory-including basic ideas of classical relations-as well as an
overview of classical logic. Because the inclusion of background
material in these classical foundations provides a self-contained
course of study, students from many different academic backgrounds
will have access to this important new theory.
- Introduction to the Concept of Fuzziness
- Classical Logic
- Classical Set Theory
- Fuzzy Sets
- Classical Relations
- Fuzzy Relations
- Fuzzy Arithmetic
- Fuzzy Logic
- Applications: A Survey
"This user-friendly text is a valuable resource to introduce
professionals from many disciplines to the broad applicability of
fuzzy set theory and fuzzy logic to many areas of human affairs.
Electrical, mechanical, and software engineers, chemists, and
managers will find this a useful tool for learning about basic
principles and ideas of the increasingly important fuzzy set theory
which later could progress to its application in their specific
fields. This book would be appropriate as a textbook for a general
course in undergraduate liberal arts and sciences programs as a
meaningful enrichment of a typical course on the basics of
classical set theory and classical logic, and as a reference source
for introductory short courses for working professionals." Prof.
Marian Stachowicz, Jack Rowe Chair, Dept. of Computer Eng., Univ.
of Minnesota
"The text provides a very carefully crafted introduction to the
basics of fuzzy sets." , Prof. Les Sztandera, Dept. of Computer
Science, Philadelphia College of Textiles and Sciences
0-13-341058-7
About the Author
Since the early 1990s, literature on fuzzy set theory and its
various applications has been rapidly growing. Hundreds of books on
this subject are now available on the market. Most of them are
either edited collections of papers on various themes or monographs
on special topics. Textbooks on fuzzy set theory are still rather
rare, in spite of the growing need for such textbooks at all levels
of higher education.
This book, Fuzzy Set Theory: Foundations and Applications, is
intended to fill a particular gap in the literature. Its aim is to
serve as a textbook for a general course in undergraduate liberal
arts and sciences programs. This aim is reflected in the content of
the book and the style in which it is written.
As the title of the book suggests, it is a simple introduction to
basic elements of fuzzy set theory. However, it also contains an
overview of the corresponding elements of classical set theory,
including basic ideas of classical relations, as well as an
overview of classical logic. The emphasis is on conceptual rather
than theoretical presentation of the material.
We hope the text will help to develop undergraduate courses in
which students will be exposed at an early stage of their studies
to basic ideas of the increasingly important fuzzy set theory. The
course may already be offered at the freshman or sophomore levels.
It may be viewed as a meaningful replacement and enrichment of a
typical course on the basics of classical set theory and classical
logic, which is often required in undergraduate liberal arts and
sciences programs.
Since the text is intended for a general course and not a course
oriented to majors in any particular discipline, it covers only the
most fundamental concepts of fuzzy set theory. Various special
topics, particularly relevant to some disciplines, are not covered.
Examples are chosen, by and large, from daily life. The broad
applicability of fuzzy set theory in many areas of human affairs is
surveyed but not covered in detail. Only a few examples of
applications are covered, chosen again from daily life.
For further study of fuzzy set theory and fuzzy logic, the
graduate text Fuzzy Sets and Fuzzy Logic: Theory and Applications
by G.J. Klir and B. Yuan (Prentice Hall, 1995) offers the most
natural continuation of this undergraduate text. The main advantage
is that both books use the same terminology and notation.
We expect that any shortcomings of this text, caused either by its
content or its style, will emerge from its use in various classroom
environments. We intend to identify them, hopefully with the help
of instructors and students using the text, and make appropriate
revisions at some time in the future. For this purpose, we welcome
any suggestions from instructors, students, or other readers of the
book.
Lastly, we would like to express our gratitude to Ms. Deborah
Stungis for reading the entire manuscript of this book and for
providing us with many useful comments, as well as to Ms. Yin Pan
for composing parts of the book and contributing to various
technical issues.
George J. Klir, Ute St.Clair, and Bo Yuan
Binghamton, New York
June 1996
From the Author
Since the early 1990s, literature on fuzzy set theory and its
various applications has been rapidly growing. Hundreds of books on
this subject are now available on the market. Most of them are
either edited collections of papers on various themes or monographs
on special topics. Textbooks on fuzzy set theory are still rather
rare, in spite of the growing need for such textbooks at all levels
of higher education.
This book, Fuzzy Set Theory: Foundations and Applications, is
intended to fill a particular gap in the literature. Its aim is to
serve as a textbook for a general course in undergraduate liberal
arts and sciences programs. This aim is reflected in the content of
the book and the style in which it is written.
As the title of the book suggests, it is a simple introduction to
basic elements of fuzzy set theory. However, it also contains an
overview of the corresponding elements of classical set theory,
including basic ideas of classical relations, as well as an
overview of classical logic. The emphasis is on conceptual rather
than theoretical presentation of the material.
We hope the text will help to develop undergraduate courses in
which students will be exposed at an early stage of their studies
to basic ideas of the increasingly important fuzzy set theory. The
course may already be offered at the freshman or sophomore levels.
It may be viewed as a meaningful replacement and enrichment of a
typical course on the basics of classical set theory and classical
logic, which is often required in undergraduate liberal arts and
sciences programs.
Since the text is intended for a general course and not a course
oriented to majors in any particular discipline, it covers only the
most fundamental concepts of fuzzy set theory. Various special
topics, particularly relevant to some disciplines, are not covered.
Examples are chosen, by and large, from daily life. The broad
applicability of fuzzy set theory in many areas of human affairs is
surveyed but not covered in detail. Only a few examples of
applications are covered, chosen again from daily life.
For further study of fuzzy set theory and fuzzy logic, the
graduate text Fuzzy Sets and Fuzzy Logic: Theory and Applications
by G.J. Klir and B. Yuan (Prentice Hall, 1995) offers the most
natural continuation of this undergraduate text. The main advantage
is that both books use the same terminology and notation.
We expect that any shortcomings of this text, caused either by its
content or its style, will emerge from its use in various classroom
environments. We intend to identify them, hopefully with the help
of instructors and students using the text, and make appropriate
revisions at some time in the future. For this purpose, we welcome
any suggestions from instructors, students, or other readers of the
book.
Lastly, we would like to express our gratitude to Ms. Deborah
Stungis for reading the entire manuscript of this book and for
providing us with many useful comments, as well as to Ms. Yin Pan
for composing parts of the book and contributing to various
technical issues.
George J. Klir, Ute St.Clair, and Bo Yuan
Binghamton, New York
June 1996
Trade Paperback
256 Pages, 5.98 x 8.98 x 0.71 in
April 17, 1997
Pearson Education
0133410587
9780133410587