Name: Mathematics Behind Fuzzy Logic
ISBN: 978-3-7908-1871-0

Overview

Authors:

Esko Turunen

Esko Turunen

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Self-containing mathematical textbook, no previous knowledge in algebra or in logic required
Contains 134 exercises with complete answers

Part of the book series: Advances in Intelligent and Soft Computing (AINSC, volume 1)

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Keywords

Algebra
Equivalence
Fuzziness
Fuzzy Logic
Fuzzy Mathematics
Fuzzy-Logik
Fuzzy-Mathematik
Many Valued Logic
Mathematik
Maxima
Soft Computing

About this book

Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses.
Chapter 1 starts from such basic concepts as order, lattice, equivalence and residuated lattice. It contains a full section on BL-algebras. Chapter 2 concerns MV-algebra and its basic properties. Chapter 3 applies these mathematical results on Lukasiewicz-Pavelka style fuzzy logic, which is studied in details; besides semantics, syntax and completeness of this logic, a lot of examples are given. Chapter 4 shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices.

Bibliographic Information

Book Title: Mathematics Behind Fuzzy Logic
Authors: Esko Turunen
Series Title: Advances in Intelligent and Soft Computing
Publisher: Physica Heidelberg
eBook Packages: Engineering, Engineering (R0)
eBook ISBN: 978-3-7908-1871-0
Series ISSN: 1867-5662
Series E-ISSN: 1867-5670
Edition Number: 1
Number of Pages: X, 191

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Mathematics Behind Fuzzy Logic