Relational Mathematics

Gunther Schmidt was a Professor in the Faculty for Informatics of the Universität der Bundeswehr München before his retirement in 2004.

• 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.

'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