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Applications of Hyperstructure Theory

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Applications of Hyperstructure Theory Cover

 

Synopses & Reviews

Publisher Comments:

This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6) automata; 7) cryptography; 8) median algebras, relation algebras; 9) combinatorics; 10) codes; 11) artificial intelligence; 12) probabilities. Audience: Graduate students and researchers.

Book News Annotation:

For graduate students and researchers in mathematics, Corsini (mathematics and computer sciences, U. of Undine, Italy) and Leoreanu (mathematics, Ai.I Cuza U., Romania) survey how hyperstructure theory, and particularly the hypergroup theory, has been applied in various areas over the past 15 years or so. Among the areas they sample are selected topics in geometry; hypergraphs and graphs; binary relations; lattices; fuzzy sets and rough sets; automata; cryptography; codes; artificial intelligence; median, relation, and algebras; and probabilities. They do not provide an index. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com)

Table of Contents

Introduction. Basic notions and results on Hyperstructure Theory. 1: Some topics of Geometry. 1. Descriptive geometries and join spaces. 2. Spherical geometries and join spaces. 3. Projective geometries and join spaces. 4. Multivalued loops and projective geometries. 2: Graphs and Hypergraphs. 1. Generalized graphs and hypergroups. 2. Chromatic quasi-canonical hypergroups. 3. Hypergroups induced by paths of a direct graph. 4. Hypergraphs and hypergroups. 5. On the hypergroup HGamma associated with a hypergraph Gamma. 6. Other hyperstructures associated with hypergraphs. 3: Binary Relations. 1. Quasi-order hypergroups. 2. Hypergroups associated with binary relations. 3. Hypergroups associated with union, intersection, direct product, direct limit of relations. 4. Relation beta in semihypergroups. 4: Lattices. 1. Distributive lattices and join spaces. 2. Lattice ordered join space. 3. Modular lattices and join spaces. 4. Direct limit and inverse limit of join spaces associated with lattices. 5. Hyperlattices and join spaces. 5: Fuzzy sets and rough sets. 2. Direct limit and inverse limit of join spaces associated with fuzzy subsets. 3. Rough sets, fuzzy subsets and join spaces. 4. Direct limits and inverse limits of join spaces associated with rough sets. 5. Hyperstructures and Factor Spaces. 6. Hypergroups induced by a fuzzy subset. Fuzzy hypergroups. 7. Fuzzy subhypermodules over fuzzy hyperrings. 8. On Chinese hyperstructures. 6: Automata. 1. Language theory and hyperstructures. 2. Automata and hyperstructures. 3. Automata and quasi-order hypergroups. 7: Cryptography. 1. Algebraic cryptography and hypergroupoids. 2. Cryptographic interpretation of some hyperstructures. 8: Codes. 1. Steiner hypergroupoids and Steiner systems. 2. Some basic notions about codes. 3. Steiner hypergroups and codes. 9: Median algebras, Relation algebras, C-algebras. 1. Median algebras and join spaces. 2. Relation algebras and quasi-canonical hypergroups. 3. C-algebras and quasi-canonical hypergroups. 10: Artificial Intelligence. 1. Generalized intervals. Connections with quasi-canonical hypergroups. 2. Weak representations of interval algebras. 11: Probabilities. Bibliography.

Product Details

ISBN:
9781402012228
Author:
Corsini, Piergiulio
Publisher:
Springer
Author:
Leoreanu, V.
Author:
Corsini, P.
Location:
Boston, MA
Subject:
Algebra - Linear
Subject:
Discrete Mathematics
Subject:
Group Theory
Subject:
Hypergroups.
Subject:
Group Theory and Generalizations
Subject:
Combinatorics
Subject:
Mathematical Logic and Foundations
Subject:
Discrete Mathematics in Computer Science
Subject:
Order, Lattices, Ordered Algebraic Structures
Subject:
Mathematics-Linear Algebra
Subject:
Algebra - Abstract
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Logic, symbolic and mathematical
Subject:
Computational complexity
Subject:
Algebra
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Advances in Mathematics
Series Volume:
5
Publication Date:
20030331
Binding:
HARDCOVER
Language:
English
Pages:
334
Dimensions:
240 x 160 mm 1440 gr

Related Subjects

Computers and Internet » Computers Reference » General
Reference » Bibliography and Library Science
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Physics » Relativity Theory

Applications of Hyperstructure Theory Used Hardcover
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Product details 334 pages Kluwer Academic Publishers - English 9781402012228 Reviews:
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