Flexible Sets and Operations on Flexible Sets
This chapter founds the fundamental theory of flexible sets. Firstly, it gives the types and definitions of flexible sets and analyzes and expounds the relationships and similarities and differences between flexible set and ordinary (rigid) set, flexible
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Principles of ImpreciseInformation Processing A New Theoretical and Technological System
Principles of Imprecise-Information Processing
Shiyou Lian
Principles of Imprecise-Information Processing A New Theoretical and Technological System
123
Shiyou Lian Xi’an Shiyou University Xi’an China
ISBN 978-981-10-1547-2 DOI 10.1007/978-981-10-1549-6
ISBN 978-981-10-1549-6
(eBook)
Library of Congress Control Number: 2016940820 © Springer Science+Business Media Singapore 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.
Preface
With the development of information and intelligence sciences and technologies as well as the rise in social requirements, imprecise-information processing about flexible linguistic values is becoming more and more important and urgent, and it will play an indispensable role in intelligent systems, especially in the anthropomorphic intelligent systems. Imprecision, which is different from uncertainty, is another independent attribute of information, and the now so-called fuzziness is actually a kind of imprecision. Therefore, the author proposed explicitly the concepts of imprecise information and imprecise-information processing, and the book, just as the title shows, is a monograph on imprecise-information processing. Actually, on imprecise-information processing, many scholars have been doing research with some results, among which the fuzzy set theory introduced by American Professor Loft Zadeh is the most famous. In fact, since Zadeh proposed the concept of fuzzy sets in 1965, the fuzzy-information processing technology based on fuzzy set theory has developed rapidly and made some achievements. However, so far, some important theoretical and technical problems in fuzzy-information processing have not been solved very well. For this reason, not a few scholars worked to improve and develop
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