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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.Read more
- A thorough reference for researchers working in a wide variety of fields
- The theory is illustrated by a wealth of exercises and practical examples
- Assumes only basic prerequisites with mathematics explained from scratch
Reviews & endorsements
"This book is an important contribution to the literature on relational algebra, especially for English speakers. Much of the work in the field has been done in German, or else maybe in English but scattered among individual papers or in volumes of proceedings. It is good to have a comprehensive, albeit very theoretical, book in English."
Anthony J. Duben, Computing ReviewsSee more reviews
"This text is deliberately encyclopedic, extremely precise and detailed, and the results aimed toward applications in areas such as psychology, linguistics, decision analysis and machine learning."
S.I. Gendler, Mathematical Reviews
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- Date Published: December 2010
- format: Hardback
- isbn: 9780521762687
- length: 582 pages
- dimensions: 234 x 156 x 32 mm
- weight: 0.99kg
- contains: 420 b/w illus. 70 exercises
- availability: Available
Table of Contents
Part I. Representations of Relations:
2. Sets, subsets and elements
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
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