Lattice-Valued Logic An Alternative Approach to Treat Fuzziness and

Lattice-valued logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. In this textbook for the first time a general introduction on lattice-valued logic is

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Springer-Verlag Berlin Heidelberg GmbH

Studies in Fuzziness and Soft Computing, Volume 132 http://www.springer.de/cgi-bin/search_book.pl?series=2941 Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail: [email protected] Further volumes of this series can be found on our homepage

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Recent Advances in Intelligent Paradigms and Applications", 2003 ISBN 3-7908-1538-1

Vol. 114. M. Fitting and E. Orowska (Eds.) Beyond Two: Theory and Applications of Multiple Valued Logic, 2003 ISBN 3-7908-1541-1 Vol. 115. J.J. Buckley

Fuzzy Probabilities, 2003 ISBN 3-7908-1542-X

Vol. 116. C. Zhou, D. MaravaH and D. Ruan (Eds.)

Autonomous Robotic Systems, 2003 ISBN 3-7908-1546-2

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Soft Computing and Fractal Theory for Intelligent Manufacturing, 2003 ISBN 3-7908-1547-0

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Entropy Measures, Maximum Entropy Principle and Emerging Applications, 2003 ISBN 3-540-00242-1

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Software Engineering with Computational Intelligence, 2003

ISBN 3-540-00472-6

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Information Fusion in Data Mining, 2003 ISBN 3-540-00676-1

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Applied Decision Support with Soft Computing, 2003 ISBN 3-540-02491-3

Vol. 125. M. Inuiguchi, S. Hirano and S. Tsumoto (Eds.)

Rough Set Theory and Granular Computing, 2003 ISBN 3-540-00574-9 Vol. 126. J.-1. Verdegay (Ed.)

Fuzzy Sets Based Heuristics for Optimization, 2003 ISBN 3-540-00551-X

Vol 127. 1. Reznik, V. Kreinovich (Eds.)

Soft Computing in Measurement and Information Acquisition, 2003 ISBN 3-540-00246-4 Vol 128. J. Casillas, O. Cord6n, F. Herrera, L. Magdalena (Eds.)

Interpretability Issues in Fuzzy Modeling, 2003 ISBN 3-540-02932-X Vol 129. J. Casillas, O. Cord6n, F. Herrera, 1. Magdalena (Eds.)

Accuracy Improvements in Linguistic Fuzzy Modeling, 2003 ISBN 3-540-02933-8 Vol 130. P.S. Nair

Uncertainty in Multi-Source Databases, 2003

ISBN 3-540-03242-8 Vol 131. J.N. Mordeson, D.S. Malik, N. Kuroki

Fuzzy Semigroups, 2003 ISBN 3-540-03243-6

Yang Xu Da Ruan Keyun Qin Jun Liu

Lattice-Valued Logic An Alternative Approach to Treat Fuzziness and Incomparability

Springer

Professor Dr. Yang Xu

Professor Dr. Da Ruan

E-mail: [email protected]

E-mail: [email protected]

Professor Dr. Keyun Qin E-mail: [email protected] Southwest Jiaotong University Department of Applied Mathematics Chengdu 610031 Sichuan PRChina

Belgian Nuclear Research Center (SCK*CEN) Boeretang 200 2400 Mal Belgium

Dr.Jun Liu The University of Manchester Institute of Science and Technology Department of Mathematics PO Box 88

Manchester M60