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Mathematical analysis --- Partially ordered sets. --- Ensembles partiellement ordonnés. --- Combinatorial set theory. --- Ensembles, Théorie combinatoire des. --- Combinatorial set theory --- Partially ordered sets --- Posets --- Sets, Partially ordered --- Ordered sets --- Set theory, Combinatorial --- Combinatorial analysis --- Set theory

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Ordered algebraic structures --- Artin rings. --- Representations of rings (Algebra) --- Partially ordered sets --- Representations of algebras --- Anneaux artiniens. --- Ensembles partiellement ordonnés. --- Représentations d'algèbres. --- Artin rings --- Rings (Algebra) --- Algebra --- Posets --- Sets, Partially ordered --- Ordered sets --- Artinian rings --- Rings, Artin --- Rings, Artinian --- Associative rings --- Commutative rings

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Semiorder is probably one of the most frequently ordered structures in science. It naturally appears in fields like psychometrics, economics, decision sciences, linguistics and archaeology. It explicitly takes into account the inevitable imprecisions of scientific instruments by allowing the replacement of precise numbers by intervals. The purpose of this book is to dissect this structure and to study its fundamental properties. The main subjects treated are the numerical representations of semiorders, the generalizations of the concept to valued relations, the aggregation of semiorders and their basic role in a general theoretical framework for multicriteria decision-aid methods. Audience: This volume is intended for students and researchers in the fields of decision analysis, management science, operations research, discrete mathematics, classification, social choice theory, and order theory, as well as for practitioners in the design of decision tools.

Besluitvorming--Problemen --- Decision problems --- Décision [Prise de ]--Problèmes --- Décision statistique --- Ensembles partiellement ordonnés --- Gedeeltelijke geordende gehelen --- Partially ordered sets --- Posets --- Sets [Partially ordered ] --- Statistical decision --- Decision making --- Prise de décision --- Mathematical models --- Modèles mathématiques --- Game theory --- Operations research --- Statistics --- Management science --- Sets, Partially ordered --- Ordered sets --- Partially ordered sets. --- Statistical decision. --- Prise de décision --- Modèles mathématiques --- Operations research. --- Decision making. --- Algebra. --- Ordered algebraic structures. --- Mathematical logic. --- Operations Research/Decision Theory. --- Order, Lattices, Ordered Algebraic Structures. --- Mathematical Logic and Foundations. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Mathematical analysis --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Research --- System theory

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This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, was first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S. Graves and K. Mark Lawrence, and to date the relevant knowledge on this subject was spread over more than two hundred research papers. Poset metrics generalizes both the standard Hamming metric – the most important metric used in the context of coding theory – and the Niederreiter-Rosenbloom-Tsfasman metric, which is an ultrametric. Conceived to be as self-contained as possible, the book starts from basic concepts of coding theory and advances towards poset proprieties and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven propositions. This work will appeal to researchers and graduate students alike, particularly those in the fields of Mathematics, Electrical Engineering and Computer Sciences, with an interest in discrete geometry and coding theory.

Partially ordered sets. --- Posets --- Sets, Partially ordered --- Ordered sets --- Algebra. --- Coding theory. --- Discrete groups. --- Number theory. --- Order, Lattices, Ordered Algebraic Structures. --- Coding and Information Theory. --- Convex and Discrete Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Groups, Discrete --- Infinite groups --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Mathematics --- Mathematical analysis --- Discrete mathematics --- Ordered algebraic structures. --- Information theory. --- Convex geometry . --- Discrete geometry. --- Geometry --- Combinatorial geometry --- Communication theory --- Communication --- Cybernetics --- Algebraic structures, Ordered --- Structures, Ordered algebraic

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The maturing of the field of data mining has brought about an increased level of mathematical sophistication. Such disciplines like topology, combinatorics, partially ordered sets and their associated algebraic structures (lattices and Boolean algebras), and metric spaces are increasingly applied in data mining research. This book presents these mathematical foundations of data mining integrated with applications to provide the reader with a comprehensive reference. Mathematics is presented in a thorough and rigorous manner offering a detailed explanation of each topic, with applications to data mining such as frequent item sets, clustering, decision trees also being discussed. More than 400 exercises are included and they form an integral part of the material. Some of the exercises are in reality supplemental material and their solutions are included. The reader is assumed to have a knowledge of elementary analysis. Features and topics: • Study of functions and relations • Applications are provided throughout • Presents graphs and hypergraphs • Covers partially ordered sets, lattices and Boolean algebras • Finite partially ordered sets • Focuses on metric spaces • Includes combinatorics • Discusses the theory of the Vapnik-Chervonenkis dimension of collections of sets This wide-ranging, thoroughly detailed volume is self-contained and intended for researchers and graduate students, and will prove an invaluable reference tool.

Data mining. --- Partially ordered sets. --- Metric spaces. --- Set theory. --- Computer science. --- Computer science --- Computer mathematics. --- Computer Science. --- Data Mining and Knowledge Discovery. --- Mathematics of Computing. --- Discrete Mathematics in Computer Science. --- Computational Mathematics and Numerical Analysis. --- Informatics --- Science --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics. --- Mathematics --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Posets --- Sets, Partially ordered --- Ordered sets --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Computational complexity. --- Complexity, Computational --- Machine theory --- Computer science—Mathematics.