Fuzzy Logic: Mathematical Tools for Approximate Reasoning by G. GerlaFuzzy Logic: Mathematical Tools for Approximate Reasoning by G. Gerla

Fuzzy Logic: Mathematical Tools for Approximate Reasoning

byG. Gerla

Paperback | December 7, 2010

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The theme of this book is fuzzy logic in a narrow sense, a promising new chapter of fuzzy logic. The basic ideas of formal logic were formulated by Lotfi Zadeh in 1975. The aim of this logic is to investigate the wonderful human capacity of reasoning with vague notions by attempting to formalize the `approximate reasoning' we use in everyday life. A peculiarity of this book is to propose a general framework based on three mathematical tools: the theory of fuzzy closure operators, an extension principle for crisp logics and the theory of recursively enumerable fuzzy subsets. This book is unique in that it treats fuzzy logics which are not truth-functional in nature (as an example, the logic of the necessities, probabilistic logics and similarity-based logics). The book is addressed to people interested in artificial intelligence, fuzzy control, formal logic, and philosophy. It can be used in special post-graduate university studies and in advanced courses. The book is completely self-contained.
Title:Fuzzy Logic: Mathematical Tools for Approximate ReasoningFormat:PaperbackDimensions:283 pages, 9.25 × 6.1 × 0 inPublished:December 7, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048156947

ISBN - 13:9789048156948

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Table of Contents

Preface. 1. Abstract logic in a lattice. 2. Abstract fuzzy logic. 3. Extending an abstract crisp logic. 4. Approximate reasoning. 5. Logic as management of constraints on the truth values. 6. Canonical extension of a crisp Hilbert logic. 7. Graded consequence relations. 8. Truth-functional logic and fuzzy logic. 9. Probabilistic fuzzy logics. 10. Fuzzy control and approximate reasoning. 11. Effectiveness in fuzzy logic. References. Index. List of symbols.

Editorial Reviews

`Gerla (University of Salerno, Italy), in this book, is concerned with fuzzy logic in the narrow sense, as the subtitle "Mathematical Tools for Approximate Reasoning" makes clear. The preface indicates that the book is principally concerned with three mathematical tools: the theory of fuzzy closure operators, an extension principle for closure operators, and the theory of recursively enumerable fuzzy subsets. Gerla sets out the details of his research related to these tools. Obviously, this book is intended for advanced study in graduate courses and as a resource for researchers, and so it would be a good addition to libraries of institutions where graduate studies and research in FLn are carried out. Graduate students and faculty' R. Bharath, emeritus, Northern Michigan University in Choice, January 2002