Relational Mathematics

ISBN-13: 9780521762687 / Angielski / Twarda / 2010 / 582 str.

Gunther Schmidt

Opis

Relational mathematics is to operations research and informatics what numerical mathematics is to engineering: it is intended to help modelling, reasoning, and computing. Its applications are therefore diverse, ranging from psychology, linguistics, decision aid, and ranking to machine learning and spatial reasoning. Although many developments have been made in recent years, they have rarely been shared amongst this broad community of researchers. This first comprehensive overview begins with an easy introduction to the topic, assuming a minimum of prerequisites; but it is nevertheless theoretically sound and up to date. It is suitable for applied scientists, explaining all the necessary mathematics from scratch using a multitude of visualised examples, via matrices and graphs. It ends with tangible results on the research level. The author illustrates the theory and demonstrates practical tasks in operations research, social sciences and the humanities.

Recenzje

'The author illustrates the mathematical theory and demonstrates practical tasks in operations research, social sciences and the humanities with graspable results at the research level. The multitude of examples is visualized using matrices and graphs. The book is suitable for applied scientists and the broad community of researchers in various fields who use relations in their scientific work.' Zentralblatt MATH

Spis treści

Preface; 1. Introduction; Part I. Representations of Relations: 2. Sets, subsets and elements; 3. Relations; Part II. Operations and Constructions: 4. Algebraic operations on relations; 5. Order and function: the standard view; 6. Relations and vectors; 7. Domain construction; Part III. Algebra: 8. Relation algebra; 9. Orders and lattices; 10. Rectangles, fringes, inverses; 11. Concept analysis; Part IV. Applications: 12. Orderings: an advanced view; 13. Preference and indifference; 14. Aggregating preferences; 15. Relational graph theory; 16. Standard Galois mechanisms; Part V. Advanced Topics: 17. Mathematical applications; 18. Implication structures; 19. Power operations; Appendix A. Notations; Appendix B. Postponed proofs of Part II; Appendix C. Algebraic visualization; Appendix D. Historical annotations; Table of symbols; References; Index.