Fuzzy Semigroups

AvJohn N. Mordeson,Davender S. Malik

Inbunden, Engelska, 2003

Del 131 i serien Studies in Fuzziness and Soft Computing

1 696 kr

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Beskrivning

The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. The book concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. Basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages are reviewed and introduced, as well as certain fuzzy ideals of a semigroup and advanced characterizations and properties of fuzzy semigroups.

Produktinformation

Utgivningsdatum:2003-07-10
Mått:155 x 235 x 23 mm
Vikt:664 g
Format:Inbunden
Språk:Engelska
Serie:Studies in Fuzziness and Soft Computing
Antal sidor:319
Upplaga:2003
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540032434

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Innehållsförteckning

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.