Fuzzy Automata and Languages

Fuzzy Automata and Languages : Theory and Applications

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Description

The huge number and broad range of the existing and potential applications of fuzzy logic have precipitated a veritable avalanche of books published on the subject. Most, however, focus on particular areas of application. Many do no more than scratch the surface of the theory that holds the power and promise of fuzzy logic.

Fuzzy Automata and Languages: Theory and Applications offers the first in-depth treatment of the theory and mathematics of fuzzy automata and fuzzy languages. After introducing background material, the authors study max-min machines and max-product machines, developing their respective algebras and exploring properties such as equivalences, homomorphisms, irreducibility, and minimality. The focus then turns to fuzzy context-free grammars and languages, with special attention to trees, fuzzy dendrolanguage generating systems, and normal forms. A treatment of algebraic fuzzy automata theory follows, along with additional results on fuzzy languages, minimization of fuzzy automata, and recognition of fuzzy languages. Although the book is theoretical in nature, the authors also discuss applications in a variety of fields, including databases, medicine, learning systems, and pattern recognition.

Much of the information on fuzzy languages is new and never before presented in book form. Fuzzy Automata and Languages incorporates virtually all of the important material published thus far. It stands alone as a complete reference on the subject and belongs on the shelves of anyone interested in fuzzy mathematics or its applications.
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Product details

  • Hardback | 576 pages
  • 165.6 x 244.3 x 36.1mm | 925.34g
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 64 Illustrations, black and white
  • 1584882255
  • 9781584882251

Table of contents

INTRODUCTION
Sets
Relations
Functions
Fuzzy Subsets
Semigroups
Finite-State Machines
Finite State Automata
Languages and Grammars
Nondeterministic Finite-State Automata
Relationships Between Languages and Automata
Pushdown Automata
MAX-MIN AUTOMATA
Max-Min Automata
General Formulation of Automata
Classes of Automata
Behavior of Max-Min Automata
Equivalences and Homomorphisms of Max-Min Automata
Reduction of Max-Min Automata
Definite Max-Min Automata
Reduction of Max-Min Machines
Equivalences
Irreducibility and Minimality
Nondeterministic and Deterministic Case
FUZZY MACHINES, LANGUAGES, AND GRAMMARS
Max-Product Machines
Equivalences
Irreducibility and Minimality
Max-Product Grammars and Languages
Weak Regular Max-Product Grammars
Weak Regular Max-Product Languages
Properties of GBP
Exercises
FUZZY LANGUAGES AND GRAMMARS
Fuzzy Languages
Types of Grammars
Fuzzy Context-Free Grammars
Context-Free Max-Product Grammars
Context-Free Fuzzy Languages
On the Description of the Fuzzy Meaning of Context-Free Languages
Trees and Pseudoterms
Fuzzy Dendrolanguage Generating Systems
Normal Form of F-CFDS
Sets of Derivation Trees of Fuzzy Context-Free Grammars
Fuzzy Tree Automaton
Fuzzy Tree Transducer
Fuzzy Meaning of Context-Free Languages
PROBABILISTIC AUTOMATA AND GRAMMARS
Probabilistic Automata and their Approximation
e-Approximating by Nonprobability Devices
e-Approximating by Finite Automata
Applications
The Pe Relation
Fuzzy Stars Acceptors and Probabilistic Acceptors
Characterizations and the Re -Relation
Probabilistic and Weighted Grammars
Probabilistic and Weighted Grammars of Type 3
Interrelations with Programmed and Time-variant Grammars
Probabilistic Grammars and Automata
Probabilistic Grammars
Weakly Regular Grammars and Asynchronous Automata
Type-0 Probabilistic Grammars and Probabilistic Turing Machines
Context-Free Probabilistic Grammars and Pushdown Automata
Realization of Fuzzy Languages by Various Automata
Properties of Lk, k - 1,2,3
Further Properties of L3
ALGEBRAIC FUZZY AUTOMATA THEORY
Fuzzy Finite State Machines
Semigroups of Fuzzy Finite State Machines
Homomorphisms
Admissible Relation
Fuzzy Transformation Semigroups
Products of Fuzzy Finite State Machines
Submachines of a Fuzzy Finite State Machine
Retrievability, Separability, and Connectivity
Decomposition of Fuzzy Finite State Machines
Subsystems of a Fuzzy Finite State Machine
Strong Subsystems
Cartesian Composition of Fuzzy Finite State Machines
Cartesian Composition
Admissible Partitions
Coverings of Products of Fuzzy Finite State Machines
Associative Properties of Products
Covering Properties of Products
Fuzzy Semiautomaton over a Finite Group
MORE ON FUZZY LANGUAGES
Fuzzy Regular Languages
On Fuzzy Recognizers
Minimal Fuzzy Recognizers
Fuzzy Recognizers and Recognizable Sets
Operation on (Fuzzy) Subsets
Construction of Recognizers and Recognizable Sets
Accessible and Coaccessible Recognizers
Complete Fuzzy Machines
Fuzzy Languages on a Free Monoid
Algebraic Character and Properties of Fuzzy Regular Languages
Deterministic Acceptors of Regular Fuzzy Languages
MINIMIZATION OF FUZZY AUTOMATA
Equivalence, Reduction, and Minimization of Finite Fuzzy Automata
Equivalence of Fuzzy Automata: An Algebraic Approach
Reduction and Minimization of Fuzzy Automata
Minimal Fuzzy Finite State Automata
Behavior, Reduction, and Minimization of Finite L-Automata
Matrices over a Bounded Chain
Systems of Linear Equivalences over a Bounded Chain
Finite L-Automata-Behavior Matrix
e-Equivalence
e-Irreducibility
Minimization
L-FUZZY AUTOMATA, GRAMMARS, AND LANGUAGES
Fuzzy Recognition of Fuzzy Languages
Fuzzy Languages
Fuzzy Recognition by Machines
Cutpoint Languages
Fuzzy Languages not Fuzzy Recognized by Machines in DT2
Rational Probabilistic Events
Recursive Fuzzy Languages
Closure Properties
Fuzzy Grammars and Recursively Enumerable Fuzzy Languages
Recursively Enumerable L-Subsets
Various Kind of Automata with Weights
APPLICATIONS
A Formulation of Fuzzy Automata and its Application as a Model of Learning Systems
Formulation of Fuzzy Automata
Special Cases of Fuzzy Automata
Fuzzy Automata as Models of Learning Systems
Applications and Simulation Results
Properties of Fuzzy Automata
Fractionally Fuzzy Grammars with Application to Pattern Recognition
Fractionally Fuzzy Grammars
A Pattern Recognition Experiment
General Fuzzy Acceptors for Syntactic Pattern Recognition
e-Equivalence by Inputs
Fuzzy-State Automata: Their Stability and Fault Tolerance
Relational Description of Automata
Fuzzy-State Automata
Stable and Almost Stable Behavior of Fuzzy-State Automata
Fault Tolerance of Fuzzy-State Automata
Clinical Monitoring with Fuzzy Automata
Fuzzy Systems
REFERENCES
INDEX

Each chapter also includes a section of exercises
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Review quote

"Self-contained, giving all necessary mathematical and language-theoretic prerequisites as well as full proofs of all presented resultsthis book presents the first general coverage of the theory of fuzzy automata and fuzzy language theory and as such will be useful not only as a textbook but also as a research monograph." -Zentralblatt MATH 1046
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