The Importance of Being Fuzzy: And Other Insights from the Border between Math and Computers

by Arturo Sangalli

Overview

In this comprehensive survey of the subject for popular science readers, Arturo Sangalli explains how computers have brought a new practicality to mathematics and its applications.

Product Details

ISBN-13:	9780691187358
Publisher:	Princeton University Press
Publication date:	06/05/2018
Sold by:	Barnes & Noble
Format:	eBook
Pages:	200
File size:	3 MB

About the Author

Arturo Sangalli is Professor of Mathematics at Champlain Regional College in Lennoxville, Québec.

Table of Contents

Preface

Acknowledgments

To the Reader

Pt. 1 Blurred Visions 1

Ch. 1 Classes with Uncertain Borders 3

Ch. 2 Fuzzy Does It 19

Pt. 2 Limits 47

Ch. 3 The Limits of Classical Computing 49

Ch. 4 The Limits of Formal Reasoning 76

Pt. 3 Natural Solutions 93

Ch. 5 Net Gains 95

Ch. 6 Solutions via Evolution 126

Afterword 157

App. 1 Fuzzy Inferences 159

App. 2 The Functions of Natural Numbers Cannot Be Enumerated 162

App. 3 The Halting Problem Is Unsolvable 164

App. 4 Learning with the Back-Propagation Algorithm 166

Index 171

What People are Saying About This

From the Publisher

"A fascinating tour of the computing of the next century. Arturo Sangalli has beautifully described the three main branches of 'soft' computing: fuzzy logic, neural networks, and genetic algorithms, in addition to reviewing the main ideas and philosophy of traditional computing. Anyone who wants to find out what the mainstream of computing will look like thirty years from now (and perhaps much sooner) must read this fascinating book."—Doron Zeilberger, winner of the Leroy P. Steele Prize for Mathematics

Doron Zeilberger

A fascinating tour of the computing of the next century. Arturo Sangalli has beautifully described the three main branches of 'soft' computing: fuzzy logic, neural networks, and genetic algorithms, in addition to reviewing the main ideas and philosophy of traditional computing. Anyone who wants to find out what the mainstream of computing will look like thirty years from now (and perhaps much sooner) must read this fascinating book.
— Doron Zeilberger, winner of the Leroy P. Steele Prize for Mathematics

Recipe

"A fascinating tour of the computing of the next century. Arturo Sangalli has beautifully described the three main branches of 'soft' computing: fuzzy logic, neural networks, and genetic algorithms, in addition to reviewing the main ideas and philosophy of traditional computing. Anyone who wants to find out what the mainstream of computing will look like thirty years from now (and perhaps much sooner) must read this fascinating book."—Doron Zeilberger, winner of the Leroy P. Steele Prize for Mathematics

Editorial Reviews

I know quite a few books on fuzzy set theory and neuro-fuzzy systems, but this work is unique. No other book have I found so pleasant to read (Even for me as a senior fuzzyist), and, at the same time, no other book seems so informative for the fuzzy or soft computing newcomer.

H. Toth

His topic is fuzzy logic, a way of representing knowledge which has become increasingly important in making computer and other artificial systems function more like humans. As its name suggests, fuzzy logic uses the imprecise possibilities of language because they capture the loosely-defined categories and generalized strategies that humans need to "learn". If you are prepared to search them out, the book does have gems. Sangelli succeeds in giving the reader an idea of the possibilities, for example, when he describes the commercial applications of fuzzy logic.
— New Scientist

Peter Thomas

Winner of the 1998 Award for Best Professional/Scholarly Book in Computer Science, Association of American Publishers

"I know quite a few books on the fuzzy set theory and neuro-fuzzy systems, but this work is unique. No other book have I found so pleasant to read and, at the same time, no other book seems so informative for the fuzzy or soft computing newcomer. . . . [T]he book presents an excellent, clear written, and easy-to-understand advertisement for fuzzy computing."—-H. Toth, Computing Reviews

"[Sangalli's] goal is to describe this recent work to a broad audience; he succeeds quite admirably. The Importance of Being Fuzzy is clear and easy to read, and yet it provides enough mathematical detail to give some appreciation for the meaning behind the metaphors."—-Mark Johnson, The Mathematical Association of America Online Book Review

From the Publisher

[Sangalli's] goal is to describe this recent work to a broad audience; he succeeds quite admirably. The Importance of Being Fuzzy is clear and easy to read, and yet it provides enough mathematical detail to give some appreciation for the meaning behind the metaphors.

The Mathematical Association of America Online Book Review - Mark Johnson

I know quite a few books on the fuzzy set theory and neuro-fuzzy systems, but this work is unique. No other book have I found so pleasant to read and, at the same time, no other book seems so informative for the fuzzy or soft computing newcomer. . . . [T]he book presents an excellent, clear written, and easy-to-understand advertisement for fuzzy computing. . . .

Computing Reviews - H. Toth

[Sangalli's] goal is to describe this recent work to a broad audience; he succeeds quite admirably. The Importance of Being Fuzzy is clear and easy to read, and yet it provides enough mathematical detail to give some appreciation for the meaning behind the metaphors.
— Mark Johnson

The Mathematical Association of America Online Book Review

I know quite a few books on the fuzzy set theory and neuro-fuzzy systems, but this work is unique. No other book have I found so pleasant to read and, at the same time, no other book seems so informative for the fuzzy or soft computing newcomer. . . . [T]he book presents an excellent, clear written, and easy-to-understand advertisement for fuzzy computing. . . .
— H. Toth

Computing Reviews