Advances in Intelligent and Soft Computing

Rough Sets

Mathematical Foundations

Authors: Polkowski, Lech

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  • ISBN 978-3-7908-1776-8
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  • Immediate eBook download after purchase
Softcover $109.99
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  • ISBN 978-3-7908-1510-8
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About this Textbook

A comprehensive introduction to mathematical structures essential for Rough Set Theory. The book enables the reader to systematically study all topics of rough set theory. After a detailed introduction in Part 1 along with an extensive bibliography of current research papers. Part 2 presents a self-contained study that brings together all the relevant information from respective areas of mathematics and logics. Part 3 provides an overall picture of theoretical developments in rough set theory, covering logical, algebraic, and topological methods. Topics covered include: algebraic theory of approximation spaces, logical and set-theoretical approaches to indiscernibility and functional dependence, topological spaces of rough sets. The final part gives a unique view on mutual relations between fuzzy and rough set theories (rough fuzzy and fuzzy rough sets). Over 300 excercises allow the reader to master the topics considered. The book can be used as a textbook and as a reference work.

Reviews

From the reviews:

"The textbook ‘Rough Sets – Mathematical Foundations’ of Lech Polkowski intends to give a complete and self-contained exposition of all the relevant material. It covers all essential results in mathematical theory of rough sets and comes with more than 320 carefully selected and commented exercises that give additional hints and background to the reader. Finally it provides a profound reference to the area of mathematical foundations of rough set theory." (Christoph Meinel, Zentralblatt MATH, Vol. 1040 (9), 2004)

"The book starts with an overview of rough sets and a bibliography on rough sets and their applications. … The book is well written. It can serve not only as a monograph, but also as a textbook; it has all the necessary math described inside, and it has over 300 exercises that help the reader master both the math and its applications to rough sets." (V. Ya. Kreinovich, Mathematical Reviews, 2004 e)


Table of contents (14 chapters)

  • Rough Set Theory: An Introduction

    Polkowski, Prof. Dr. Lech

    Pages 3-92

  • The Sentential Calculus

    Polkowski, Prof. Dr. Lech

    Pages 95-120

  • Logical Theory of Approximations

    Polkowski, Prof. Dr. Lech

    Pages 121-136

  • Many—Valued Sentential Calculi

    Polkowski, Prof. Dr. Lech

    Pages 137-158

  • Propositional Modal Logic

    Polkowski, Prof. Dr. Lech

    Pages 159-172

Buy this book

eBook $84.99
price for Mexico (gross)
  • ISBN 978-3-7908-1776-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.99
price for Mexico
  • ISBN 978-3-7908-1510-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Rough Sets
Book Subtitle
Mathematical Foundations
Authors
Series Title
Advances in Intelligent and Soft Computing
Series Volume
15
Copyright
2002
Publisher
Physica-Verlag Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-7908-1776-8
DOI
10.1007/978-3-7908-1776-8
Softcover ISBN
978-3-7908-1510-8
Series ISSN
1867-5662
Edition Number
1
Number of Pages
XIX, 534
Number of Illustrations and Tables
3 b/w illustrations
Topics