Approximate Reasoning by Parts An Introduction to Rough Mereology

--- PLEASE take the tex- version ---The monograph offers a view on Rough Mereology, a tool for reasoning under uncertainty, which goes back to Mereology, formulated in terms of  parts by Lesniewski, and borrows from Fuzzy Set Theory and Rough Set The

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Intelligent Systems Reference Library, Volume 20 Editors-in-Chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail: [email protected]

Prof. Lakhmi C. Jain University of South Australia Adelaide Mawson Lakes Campus South Australia 5095 Australia E-mail: [email protected]

Further volumes of this series can be found on our homepage: springer.com Vol. 1. Christine L. Mumford and Lakhmi C. Jain (Eds.) Computational Intelligence: Collaboration, Fusion and Emergence, 2009 ISBN 978-3-642-01798-8

Vol. 11. Samuli Niiranen and Andre Ribeiro (Eds.) Information Processing and Biological Systems, 2011 ISBN 978-3-642-19620-1

Vol. 2. Yuehui Chen and Ajith Abraham Tree-Structure Based Hybrid Computational Intelligence, 2009 ISBN 978-3-642-04738-1

Vol. 12. Florin Gorunescu Data Mining, 2011 ISBN 978-3-642-19720-8

Vol. 3. Anthony Finn and Steve Scheding Developments and Challenges for Autonomous Unmanned Vehicles, 2010 ISBN 978-3-642-10703-0 Vol. 4. Lakhmi C. Jain and Chee Peng Lim (Eds.) Handbook on Decision Making: Techniques and Applications, 2010 ISBN 978-3-642-13638-2 Vol. 5. George A. Anastassiou Intelligent Mathematics: Computational Analysis, 2010 ISBN 978-3-642-17097-3

Vol. 13. Witold Pedrycz and Shyi-Ming Chen (Eds.) Granular Computing and Intelligent Systems, 2011 ISBN 978-3-642-19819-9 Vol. 14. George A. Anastassiou and Oktay Duman Towards Intelligent Modeling: Statistical Approximation Theory, 2011 ISBN 978-3-642-19825-0 Vol. 15. Antonino Freno and Edmondo Trentin Hybrid Random Fields, 2011 ISBN 978-3-642-20307-7

Vol. 6. Ludmila Dymowa Soft Computing in Economics and Finance, 2011 ISBN 978-3-642-17718-7

Vol. 16. Alexiei Dingli Knowledge Annotation: Making Implicit Knowledge Explicit, 2011 ISBN 978-3-642-20322-0

Vol. 7. Gerasimos G. Rigatos Modelling and Control for Intelligent Industrial Systems, 2011 ISBN 978-3-642-17874-0

Vol. 17. Crina Grosan and Ajith Abraham Intelligent Systems, 2011 ISBN 978-3-642-21003-7

Vol. 8. Edward H.Y. Lim, James N.K. Liu, and Raymond S.T. Lee Knowledge Seeker – Ontology Modelling for Information Search and Management, 2011 ISBN 978-3-642-17915-0

Vol. 18. Achim Zielesny From Curve Fitting to Machine Learning, 2011 ISBN 978-3-642-21279-6

Vol. 9. Menahem Friedman and Abraham Kandel Calculus Light, 2011 ISBN 978-3-642-17847-4

Vol. 19. George A. Anastassiou Intelligent Systems: Approximation by Artificial Neural Networks, 2011 ISBN 978-3-642-21430-1

Vol. 10. Andreas Tolk and Lakhmi C. Jain Intelligence-Based Systems Engineering, 2011 ISBN 978-3-642-17930-3

Vol. 20. Lech Polkowski Approximate Reasoning by Parts, 2011 ISBN 978-3-642-22278-8

Lech Polkowski

Approximate Reasoning by Parts An Introduction to Rough Mereology

123

Prof. dr. Lech Polkowski Polish-Japanese Institute of Information Technology and University of Warmia and Mazury Koszykowa 86 02–008 Warszawa, Poland E-mail: [email protected]

ISBN 978-3-642-22278-8

e-ISBN 978-3-642-22279-5

DOI 10.1007/978-3-642-22279-5 Intelligent Syst