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Rough Sets

Mathematical Foundations

  • Lech Polkowski

Part of the Advances in Soft Computing book series (AINSC, volume 15)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Rough Sets

    1. Front Matter
      Pages 1-1
    2. Lech Polkowski
      Pages 3-92
  3. Prerequisites

    1. Front Matter
      Pages 93-93
    2. Lech Polkowski
      Pages 95-120
    3. Lech Polkowski
      Pages 121-136
    4. Lech Polkowski
      Pages 137-158
    5. Lech Polkowski
      Pages 159-172
    6. Lech Polkowski
      Pages 173-212
    7. Lech Polkowski
      Pages 213-250
    8. Lech Polkowski
      Pages 251-272
    9. Lech Polkowski
      Pages 273-296
  4. Mathematics of Rough Sets

    1. Front Matter
      Pages 297-297
    2. Lech Polkowski
      Pages 299-330
    3. Lech Polkowski
      Pages 331-360
    4. Lech Polkowski
      Pages 361-410
  5. Rough vs. Fuzzy

    1. Front Matter
      Pages 411-411
    2. Lech Polkowski
      Pages 413-464
    3. Lech Polkowski
      Pages 465-500
  6. Back Matter
    Pages 501-534

About this book

Introduction

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.

Keywords

Fuzzy Set Theory Fuzzy Sets Mathematical Foundations Rough Sets Rough Sets Theory fuzzy set theory

Authors and affiliations

  • Lech Polkowski
    • 1
    • 2
  1. 1.Polish-Japanese Institute of Information TechnologyWarsawPoland
  2. 2.Department of Mathematics and Computer ScienceUniversity of Wormia and MazuryOlsztynPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7908-1776-8
  • Copyright Information Physica-Verlag Heidelberg 2002
  • Publisher Name Physica, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-7908-1510-8
  • Online ISBN 978-3-7908-1776-8
  • Series Print ISSN 1867-5662
  • Series Online ISSN 1867-5670
  • Buy this book on publisher's site