Relational Mathematics: 132 (Encyclopedia of Mathematics and its Applications, Series Number 132)
Cambridge University Press
Edition: Illustrated, 11/4/2010
EAN 9780521762687, ISBN10: 0521762685
Hardcover, 582 pages, 23.4 x 15.5 x 3.3 cm
Language: English
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 comprehensive 2010 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.
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.