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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.
List of contents
1 Rough Set Theory: An Introduction.- 2 The Sentential Calculus.- 3 Logical Theory of Approximations.- 4 Many-Valued Sentential Calculi.- 5 Propositional Modal Logic.- 6 Set Theory.- 7 Topological Structures.- 8 Algebraic Structures.- 9 Predicate Calculus.- 10 Independence, Approximation.- 11 Topology of Rough Sets.- 12 Algebra and Logic of Rough Sets.- 13 Infinite-valued Logical Calculi.- 14 From Rough to Fuzzy.- List of Symbols.
Summary
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.
Additional text
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)
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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)
