Fuzzy Relational Systems Foundations and Principles

Name: Fuzzy Relational Systems Foundations and Principles
Price: 75.0 USD
Availability: InStock
ISBN: 9780306467776

ISBN-10: 0306467771

ISBN-13: 9780306467776

Edition: 2002

Authors: Radim Belohlï¿½vek

List price: $169.99

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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"…

Book details

List price: $169.99
Copyright year: 2002
Publisher: Springer
Publication date: 6/30/2002
Binding: Hardcover
Pages: 369
Size: 7.01" wide x 10.00" long x 1.00" tall
Weight: 4.598
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