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  • Textbook
  • © 2002

Rough Sets

Mathematical Foundations

Authors:

  • First book on the foundations of rough sets since 10 years
  • Presents deep theoretical results in the book form for the first time
  • Over 300 exercises and an extensive bibliography with all relevant works and current research
  • Self-contained structure providing all relevant information from respective areas of mathematics and logics
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xix
  2. Rough Sets

    1. Front Matter

      Pages 1-1
    2. Rough Set Theory: An Introduction

      • Lech Polkowski
      Pages 3-92
  3. Prerequisites

    1. Front Matter

      Pages 93-93
    2. The Sentential Calculus

      • Lech Polkowski
      Pages 95-120
    3. Logical Theory of Approximations

      • Lech Polkowski
      Pages 121-136
    4. Many—Valued Sentential Calculi

      • Lech Polkowski
      Pages 137-158
    5. Propositional Modal Logic

      • Lech Polkowski
      Pages 159-172
    6. Set Theory

      • Lech Polkowski
      Pages 173-212
    7. Topological Structures

      • Lech Polkowski
      Pages 213-250
    8. Algebraic Structures

      • Lech Polkowski
      Pages 251-272
    9. Predicate Calculus

      • Lech Polkowski
      Pages 273-296
  4. Mathematics of Rough Sets

    1. Front Matter

      Pages 297-297
    2. Independence, Approximation

      • Lech Polkowski
      Pages 299-330
    3. Topology of Rough Sets

      • Lech Polkowski
      Pages 331-360
    4. Algebra and Logic of Rough Sets

      • Lech Polkowski
      Pages 361-410
  5. Rough vs. Fuzzy

    1. Front Matter

      Pages 411-411
    2. Infinite—valued Logical Calculi

      • Lech Polkowski
      Pages 413-464
    3. From Rough to Fuzzy

      • Lech Polkowski
      Pages 465-500
  6. Back Matter

    Pages 501-534

About this book

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)

Authors and Affiliations

  • Polish-Japanese Institute of Information Technology, Warsaw, Poland

    Lech Polkowski

  • Department of Mathematics and Computer Science, University of Wormia and Mazury, Olsztyn, Poland

    Lech Polkowski

Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access