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Fuzzy Automata and Languages

Theory and Applications

Fuzzy Automata and Languages by John N. Mordeson
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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 £
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
CRC Press; March 2002
577 pages; ISBN 9781420035643
Read online, or download in secure PDF format
Title: Fuzzy Automata and Languages
Author: John N. Mordeson; Davender S. Malik
 
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