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Fuzzy Relational Systems Foundations and Principles

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ISBN-10: 0306467771

ISBN-13: 9780306467776

Edition: 2002

Authors: Radim Belohl�vek

List price: $269.00
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Description:

This book deals with fuzzy relational systems, i.e. with systems of fuzzy relations defined on a set. Fuzzy relational systems represent mathematical framework for fuzzy relational modeling which is the most successful part of fuzzy logic. The book deals with foundational aspects of fuzzy relational systems. It starts (Chapter 2) with motivations and discussions about fuzzy approach. The result of this are some requirements for the structures of truth values for fuzzy logic. These structures are analyzed in subsequent sections. Chapter 3 is a key one and develops a general theory of fuzzy relational systems, paying special attention to issues which are degenerate in classical "non-fuzzy" case. Chapter 4 deals with binary fuzzy relations and particularly with similarity and order, two most frequently used types of binary relations. Chapter 5 deals with binary fuzzy relations (interpreted as fuzzy relations between a set of objects and a set of attributes) and formal analysis of such relations. Chapter 6 focuses on the problem of composition and decomposition of binary fuzzy relations. Chapter 7 contains miscellaneous topics: fuzzy closure operators, similarity spaces, selected applications, and a formal deductive system of fuzzy logic. Each Chapter is closed by bibliographical remarks. The book contains a bibliography and an index of key terms. The book provides a general framework for dealing with fuzzy relational systems and brings several new results.
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Book details

List price: $269.00
Copyright year: 2002
Publisher: Springer
Publication date: 6/30/2002
Binding: Hardcover
Pages: 369
Size: 6.75" wide x 10.00" long x 1.00" tall
Weight: 2.046
Language: English

Preliminaries
Sets, relations, mappings
Ordered sets, lattices
Tolerances, equivalences
Algebras
Fuzzy Approach, Graded Truth, and Structures of Truth Values
Fuzzy approach: from resolving paradoxes to engineering applications
Graded truth and structures of truth values
Residuated lattices
Residuated lattices and t-norms
Fuzzy Structures
Fuzzy sets and fuzzy relations
Fuzzy logic: syntax and semantics
Similarity issues
Morphisms, products, substructures
Representation by crisp structures: cutlike semantics
Algebras with fuzzy equalities
Many-sorted case
Binary Fuzzy Relations
Operations and properties of binary fuzzy relations
Similarity: fuzzy equivalences
Hierarchy: fuzzy order
Object-Attribute Fuzzy Relations and Fuzzy Concept Lattices
Conceptual granulation: fuzzy context, fuzzy concepts, and fuzzy concept lattice
Similarity and logical precision
Fuzzy Galois connections
Main theorem of fuzzy concept lattices
Composition and Decomposition of Fuzzy Relations
Composition of fuzzy relations
Decomposition: fuzzy relational equations
Miscellanea
Fuzzy closure operators and similarity spaces
Applications of selected results to some problems and models
Fuzzy logic with truth degrees in residuated lattices
References
Index