Progress in Fuzzy Sets and Systems
This volume contains the proceedings of the Second Joint IFSA-EC and EURO-WGFS Workshop on Progress in Fuzzy Sets in Europe held on April 6 -8, 1989 in Vienna, Austria. The workshop was organized by Prof. Dr. Wolfgang H. Janko from the University of Econo
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THEORY AND DECISION LIBRARY General Editors: W. Leinfellner and G. Eberlein Series A: Philosophy and Methodology of the Social Sciences Editors: W. Leinfellner (Technical University of Vienna) G. Eberlein (Technical University of Munich) Series B: Mathematical and Statistical Methods Editor: H. Skala (University ofPaderbom) Series C: Game Theory, Mathematical Programming and Operations Research Editor: S. H. Tijs (University of Nijmegen) Series D: System Theory, Knowledge Engineering and Problem Solving Editor: W. Janko (University of Economics, Vienna)
SERIES D: SYSTEM THEORY, KNOWLEDGE ENGINEERING AND
PROBLEM SOLVING
Editor: W. Janko (Vienna) Volume 5
Editorial Board G. Feichtinger (Vienna), H. T. Nguyen (Las Cruces), N. B. Nicolau (palma de Mallorca), o. Opitz (Augsburg), H. J. Skala (paderbom), M. Sugeno (Yokohama). Scope This series focuses on the design and description of organisations and systems with application to the social sciences. Formal treatment of the subjects is encouraged. Systems theory, information systems, system analysis, interrelated structures, program systems and expert systems are considered to be a theme within the series. The fundamental basics of such concepts including computational and algorithmic aspects and the investigation of the empirical behaviour of systems and organisations will be an essential part of this library. The study of problems related to the interface of systems and organisations to their environment is supported. Interdisciplinary considerations are welcome. The publication of recent and original results will be faVOured.
For a list of titles published in this series, see final page.
PROGRESS IN FUZZY SETS
AND SYSTEMS
edited by WOLFGANG H. JANKO Department ofApplied Computer Science, University of Vienna, Austria MARC ROUBENS Faculte Polytechnique de Mons, Belgium
and H.-J. ZIMMERMANN Aachen Institute of Technology, F.R.G.
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
Library of Congress Cataloging in Publication Data Progress in fuzzy sets and systems I edited by Wolfgang H. Janko, Marc Roubens, H.-J. Zimmermann. p. cm. -- erg Mining Academy Department of Mathematics
P. O. Box 47
9200 FreirJerg, GDR
ABSTRACT. In t,hiE; case study we demonstrate with an example of practical import.OQlce how eA-periment,al results, given via blurred pi.ct,ures, can be specified by fuzzy observations and used to evaluate functional relationships. The computation Js performed by ITIt"'AnS of the linage processing equipment ROBOTRON A 6471. 1. INTRODUCTION Usually the results of nlP-Etsurements or observat,ions" shortly da.1&, are recorded as points in an appropriate feature space. To t,ake Jnto account, their ever present inaccuracy and l;U1certainty, they ."Ire then cons:idered as realizations of certain random elements. In order to investigate what functional relationship is, approximately, satisfied by the data, we have, as a rule, to specify a family of functions, a so-called ~, from which we want to use a function as an approximation of the unknown funct
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