Applications of Fuzzy Sets to Systems Analysis
Ten years ago, Zadeh has brought into vogue the use of a name. Scientists no is an increasing less than poets strike off words that fit a situation. Today there recognition that for understanding vagueness, a fuzzy approach is required. We are just going
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c. V. Negoitci
D. A. Ralescu
Applications of Fuzzy Sets to Systems Analysis
Springer Basel AG 1975
First published under C. V. Negoiţă, D. A. Ralescu Mulţimi vagi şi aplicaţiile lor © Editura tehnică, 1974 Bucureşti - Piaţa Scînteii nr. 1 România
English translation © 1975 by Springer Basel AG Originally published by Birkhăuser Verlag Basel in 1975 Softcover reprint ofthe hardcover Ist edition 1975 (Interdisciplinary Systems Research, VoI. 11) ISBN 978-3-7643-0789-9 AII rights reserved. No part of this book may be reproduced by any means, nor transmitted, nor translated into a machine language without the written permission of the publisher. Library of Congress Cataloging in Publication Data Constanti n Virgil Applications of fuzzy sets to systems analysis Negoiţă,
Translation of Mulţimi vagi şi aplicaţiile lor "A Halsted Press book" Bibliography: p. J. Set theory. 2. System analysis. 3. Sequential machine theory. I. Raleseu, D. A., joint author. II. Title QA248.N4313 511'.3 75 -35789
ISBN 978-3-7643-0789-9 ISBN 978-3-0348-5921-9 (eBook) DOI 10.1007/978-3-0348-5921-9 Published in the U.S.A., Canada and Latin America by Halsted Press, a Division of John Wiley & Sons, Inc., New York
PREFACE
Ten years ago, Zadeh has brought into vogue the use of a name. Scientists no less than poets strike off words that fit a situation. Today there is an increasing recognition that for understanding vagueness, a fuzzy approach is required. We are just going through ~ transient period. From discussions of general philosophy to practical methods for system analysis. Unfortunately, much of the existing research is scattered. The practitioner interested in these methods face the challenge of sorting through a vast amount of literature to find a core on which to build. One of the objects of this book was to facilitate communication by bringing together different viewpoints and coloring them from a common viewpoint. Since the romanian version appeared, at the very beginning of 1974, there has been a rapid growth in the literature of fuzzy modelling. A minor revision would have left the book quite out-of-date. The opportunity has been taken to correct, clarify, and update. Inexactness is implicit in human behaviour and erare humanum est. It is a pleasure to acknowledge the help we have received in preparing this version. The opportunity to see an english edition was a powerful stimulus, and we are grateful to Salomon Klaczko for making this possible. Another debt is to all fuzzy authors we have quoted. Their fascinating papers kindled our interest in the subject. Bucharest, May 1975
Dr. C. V. NEGOITA
TABLE OF CONTENTS
Introduction . . . . . . .
9
1. Fuzzy sets, L-sets, flou sets
12
1-1. The lattice of fuzzy subsets . . . . . 1-3. Flou sets and L-sets 1-4. Fuzzy sets and probabilities 1-5. Categories Set(L), Setg(L), Setg(L) 1- 6. Historical and bibliographical remarks
1- 2. Fuzzy functions
2. Fuzzy theories
2 -1. 2 - 2. 2-3. 2-4. 2-5.
Fuzzy categories . . . . Fuzzy topological spaces Fuzzy structures . . . Fuzzy char
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