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Author:   John N. Mordeson ,  Davender S. Malik ,  Nobuaki Kuroki
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2003
Volume:   131
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.510kg
ISBN:  

9783642057069

ISBN 10:   3642057063
Pages:   319
Publication Date:   05 December 2010
Audience:   Professional and scholarly ,  College/higher education ,  Professional & Vocational ,  Tertiary & Higher Education
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- 1.1 Notation.- 1.2 Relations.- 1.3 Functions.- 1.4 Fuzzy Subsets.- 1.5 Semigroups.- 1.6 Codes.- 1.7 Finite-State Machines.- 1.8 Finite-State Automata.- 1.9 Languages and Grammars.- 1.10 Nondeterministic Finite-State Automata.- 1.11 Relationships Between Languages and Automata.- 2 Fuzzy Ideals.- 2.1 Introduction.- 2.2 Ideals in Semigroups.- 2.3 Fuzzy Ideals in Semigroups.- 2.4 Fuzzy Bi-ideals in Semigroups.- 2.5 Fuzzy Interior Ideals in Semigroups.- 2.6 Fuzzy Quasi-ideals in Semigroups.- 2.7 Fuzzy Generalized Bi-ideals in Semigroups.- 2.8 Fuzzy Ideals Generated by Fuzzy Subsets of Semigroups.- 3 Regular Semigroups.- 3.1 Regular Semigroups.- 3.2 Completely Regular Semigroups.- 3.3 Intra-regular Semigroups.- 3.4 Semisimple Semigroups.- 3.5 On Fuzzy Regular Subsemigroups of a Semigroup.- 3.6 Fuzzy Weakly Regular Subsemigroups.- 3.7 Fuzzy Completely Regular and Weakly Completely Regular Subsemigroups.- 3.8 Weakly Regular Semigroups.- 4 Semilattices of Groups.- 4.1 A Semilattice of Left (Right) Simple Semigroups.- 4.2 A Semilattice of Left (Right) Groups.- 4.3 A Semilattices of Groups.- 4.4 Fuzzy Normal Semigroups.- 4.5 Convexity and Green’s Relations.- 4.6 The Compact Convex Set of Fuzzy Ideals.- 4.7 Fuzzy Ideals and Green’s Relations.- 5 Fuzzy Congruences on Semigroups.- 5.1 Fuzzy Congruences on a Semigroup.- 5.2 Fuzzy Congruences on a Group.- 5.3 Fuzzy Factor Semigroups.- 5.4 Homomorphism Theorems.- 5.5 Idempotent-separating Fuzzy Congruences.- 5.6 Group Fuzzy Congruences.- 5.7 The Lattice of Fuzzy Congruence Relations on a Semigroup.- 5.8 Fuzzy Congruence Pairs of Inverse Semigroups.- 5.9 Fuzzy Rees Congruences on Semigroups.- 5.10 Additional Fuzzy Congruences on Semigroups.- 6 Fuzzy Congruences on T*-pure Semigroups.- 6.1 T*-pure Semigroups.- 6.2Semilattice Fuzzy Congruences.- 6.3 Group Fuzzy Congruences.- 7 Prime Fuzzy Ideals.- 7.1 Preliminaries.- 7.2 Prime Fuzzy Ideals.- 7.3 Weakly Prime Fuzzy Ideals.- 7.4 Completely Prime and Weakly Completely Prime Fuzzy Ideals.- 7.5 Relationships.- 7.6 Types of Prime Fuzzy Left Ideals.- 7.7 Prime Fuzzy Left Ideals.- 7.8 Fuzzy m-systems and Quasi-prime Fuzzy Left Ideals.- 7.9 Weakly Quasi-prime Fuzzy Left Ideals.- 7.10 Fuzzy Ideals i(f) and I(f).- 7.11 Strongly Semisimple Semigroups.- 7.12 Fuzzy Multiplication Semigroups.- 7.13 Properties of Fuzzy Multiplication Semigroups.- 7.14 Fuzzy Ideal Extensions.- 7.15 Prime Fuzzy Ideals.- 8 Fuzzy Codes on Free Monoids.- 8.1 Fuzzy Codes.- 8.2 Prefix Codes.- 8.3 Maximal Fuzzy Prefix Codes.- 8.4 Algebraic Properties of Fuzzy Prefix Codes on a Free Monoid.- 8.5 Fuzzy Prefix Codes Related to Fuzzy Factor Theorems.- 8.6 Equivalent Depictions of Fuzzy Codes.- 8.7 Fuzzy Codes and Fuzzy Submonoids.- 8.8 An Algorithm of test for Fuzzy Codes.- 8.9 Measure of a Fuzzy Code.- 8.10 Code Theory and Fuzzy Subsemigroups.- 8.11 Construction of Examples by Closure Systems.- 8.12 Examples by *-morphisms.- 9 Generalized State Machines.- 9.1 T-generalized State Machines.- 9.2 T-generalized Transformation Semigroups.- 9.3 Coverings.- 9.4 Direct Products.- 9.5 Decompositions of T-generalized Transformation Semigroups.- 9.6 On Proper Fuzzification of Finite State Machines.- 9.7 Generalized Fuzzy Finite State Machines.- 9.8 Fuzzy Relations and Fuzzy Finite State Machines.- 9.9 Completion of Fuzzy Finite State Machines.- 9.10 Generalized State Machines and Homomorphisms.- 10 Regular Fuzzy Expressions.- 10.1 Regular Fuzzy Expressions.- 10.2 Codes Over Languages.- 10.3 Regulated Codes and Fuzzy Grammars.- References.

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