Fuzzy Automata and Languages

Fuzzy Automata and Languages : Theory and Applications

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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.show more

Product details

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

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 1046show more

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 exercisesshow more

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