Relational mathematics / Gunther Schmidt.

Includes bibliographical references and index.

A modern, comprehensive overview providing an easy introduction for applied scientists who are not versed in mathematics.

Print version record.

Cover; Half Title; Series Page; Title; Copyright; Contents; Notes on illustrations; Preface; 1 Introduction; PART I: REPRESENTATIONS OF RELATIONS; 2 Sets, subsets, and elements; 2.1 Set representation; 2.2 Element representation; 2.3 Subset representation; 3 Relations; 3.1 Relation representation; 3.2 Relations describing graphs; 3.3 Relations generated by cuts; 3.4 Relations generated randomly; 3.5 Function representation; 3.6 Permutation representation; 3.7 Partition representation; PART II: OPERATIONS AND CONSTRUCTIONS; 4 Algebraic operations on relations; 4.1 Typing relations.

4.2 Boolean operations4.3 Relational operations proper; 4.4 Composite operations; 5 Order and function: the standard view; 5.1 Functions; 5.2 Mappings and points; 5.3 Order and strictorder; 5.4 Equivalence and quotient; 5.5 Transitive closure; 5.6 Congruences; 5.7 Homomorphisms; 6 Relations and vectors; 6.1 Domain and codomain; 6.2 Rectangular zones; 6.3 Independent pair of sets and covering pair of sets; 6.4 Reducing vectors; 6.5 Progressively infinite subsets; 6.6 Stable and absorbant sets; 7 Domain construction; 7.1 Domains of ground type; 7.2 Direct product; 7.3 Direct sum.

7.4 Quotient domain7.5 Subset extrusion; 7.6 Direct power; 7.7 Domain permutation; 7.8 Remarks on further constructions; 7.9 Equivalent representations; PART III ALGEBRA; 8 Relation algebra; 8.1 Laws of relation algebra; 8.2 Visualizing the algebraic laws; 8.3 Elementary properties of relations; 8.4 Cancellation properties of residuals and cones; 8.5 Cancellation properties of the symmetric quotient; 8.6 Tarski rule and Point Axiom; 9 Orders and lattices; 9.1 Maxima and minima; 9.2 Bounds and cones; 9.3 Least and greatest elements; 9.4 Greatest lower and least upper bounds; 9.5 Lattices.

10 Rectangles, fringes, inverses10.1 Non-enlargeable rectangles; 10.2 Independent pairs and covering pairs of sets; 10.3 Fringes; 10.4 Difunctional relations; 10.5 Ferrers relations; 10.6 Block-transitive relations; 10.7 Inverses; 11 Concept analysis; 11.1 Row and column spaces; 11.2 Factorizations; 11.3 Concept lattices; 11.4 Closure and contact; 11.5 Completion of an ordering; PART IV APPLICATIONS; 12 Orderings: an advanced view; 12.1 Additional properties of orderings; 12.2 The hierarchy of orderings; 12.3 Block-transitive strictorders; 12.4 Order extensions.

12.5 Relating preference and utility12.6 Intervalorders and interval graphs; 13 Preference and indifference; 13.1 Duality; 13.2 Modelling indifference; 13.3 Modelling thresholds; 13.4 Preference structures; 14 Aggregating preferences; 14.1 Modelling preferences; 14.2 Introductory example; 14.3 Relational measures; 14.4 Relational integration; 14.5 Defining relational measures; 14.6 De Morgan triples; 15 Relational graph theory; 15.1 Reducibility and irreducibility; 15.2 Homogeneous difunctional relations; 15.3 Subsets characterized by relational properties; 16 Standard Galois mechanisms.

English.

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