Applications of Category Theory to Fuzzy Subsets

This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. First, this volume is an extended account of the eleventh Seminar of 1989. Second, and more importantly, it is the culmination

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THEORY AND DECISION LIBRARY

General Editors: W. Leinfellner (Vienna) and G. Eberlein (Munich) Series A: Philosophy and Methodology of the Social Sciences Series B: Mathematical and Statistical Methods Series C: Game Theory, Mathematical Programming and Operations Research Series D: System Theory, Knowledge Engineering and Problem Solving

SERIES B: MATHEMATICAL AND STATISTICAL METHODS VOLUME 14

Editor: H. J. Skala (paderborn); Assistant Editor: M. Kraft (paderborn); Editorial Board: J. Aczel (Waterloo, Ont.), G. Bamberg (Augsburg), H. Drygas (Kassel), W. Eichhorn (Karlsruhe), P. Fishburn (Murray Hill, N.J.), D. Fraser (Toronto), W. Janko (Vienna), P. de Jong (Vancouver), T. Kariya (Tokyo), M. Machina (La Jolla, Calif.), A. Rapoport (Toronto), M. Richter (Kaiserslautern), B. K. Sinha (Cattonsville, Md.), D. A. Sprott (Waterloo, Ont.), P. Suppes (Stanford, Calif.), H. Theil (Gainesville, Fla.), E. Trillas (Madrid), L. A. Zadeh (Berkeley, Calif.).

Scope: The series focuses on the application of methods and ideas of logic, mathematics and statistics to the social sciences. In particular, formal treatment of social phenomena, the analysis of decision making, information theory and problems of inference will be central themes of this part of the library. Besides theoretical results, empirical investigations and the testing of theoretical models of real world problems will be subjects of interest. In addition to emphasizing interdisciplinary communication, the series will seek to support the rapid dissemination of recent results.

The titles published in this series are listed at the end of this volume.

APPLICATIONS OF CATEGORY THEORY TO FUZZY SUBSETS edited by

S1EPHEN ERNEST RODABAUGH Department of Mathematical and Computer Sciences, Youngstown State University, Youngstown, Ohio, U.SA.

ERICH PETER KLEMENT Institut fur Mathematik, Johannes Kepler Universitiit, Linz, Austria

and ULRICH HOHLE Fachbereich Mathematik, Bergische Universitiit, Wuppertal, Germany

..

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

Library of Congress Cataloging-in-Publication Data Applications of category theory to fuzzy subsets / edited by Stephen Ernest Rodabaugh, Erich Peter Klement, Ulrich Hohle. p. cm. -- (Theory and decis ion library. Series B, Mathematical and statistical lIIethods ; v. 14) The .aterial of this book has close relationship to the Eleventh International Seminar on Fuzzy Set Theory held in Linz, Austria, 19B9. Inc 1udes index. ISBN 978-94-010-5156-9 ISBN 978-94-011-2616-8 (eBook) DOI 10.1007/978-94-011-2616-8

1. Fuzzy sets--Congresses. 2. Categories (Mathematics)-Congresses. 1. Rodabaugh, Stephen Ernest. II. Klement, E. P. (Erich Peter) III. Hohle, Ulrich. IV. International Seminar on Fuzzy Set Theory (1lth , 1989 , Linz, Austria) V. Series. CA248.A76 1991 511.3'22--dc20 91-34781

ISBN 978-94-010-5156-9

Printed on acid-free paper

AII Rights Reserved 1992 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1992 Softcover reprint ofthe hardcover Ist edition 1992 No part of the m