This book describes Python3 programming resources for implementing decision aiding algorithms in the context of a bipolar-valued outranking approach. These computing resources, made available under the name Digraph3, are useful in the field of Algorithmic Decision Theory and more specifically in outranking-based Multiple-Criteria Decision Aiding (MCDA). The first part of the book presents a set of tutorials introducing the Digraph3 collection of Python3 modules and its main objects, such as bipolar-valued digraphs and outranking digraphs. In eight methodological chapters, the second part illustrates multiple-criteria evaluation models and decision algorithms. These chapters are largely problem-oriented and demonstrate how to edit a new multiple-criteria performance tableau, how to build a best choice recommendation, how to compute the winner of an election and how to make rankings or ratings using incommensurable criteria.The book's third part presents threereal-world decision case studies, while the fourth part addresses more advanced topics, such as computing ordinal correlations between bipolar-valued outranking digraphs, computing kernels in bipolar-valued digraphs, testing for confidence or stability of outranking statements when facing uncertain or solely ordinal criteria significance weights, and tempering plurality tyranny effects in social choice problems. The fifth and last part is more specifically focused on working with undirected graphs, tree graphs and forests. The closing chapter explores comparability, split, interval and permutation graphs.

The book is primarily intended for graduate students in management sciences, computational statistics and operations research. The chapters presenting algorithms for ranking multicriteria performance records will be of computational interest for designers of web recommender systems. Similarly, the relative and absolute quantile-rating algorithms, discussed and illustrated in several chapters, will be of practical interest to public and private performance auditors.

Autorentext

Raymond Bisdorff holds a degree in Business Administration from the University of Liège, Belgium, a Ph.D. in Operations Research (OR) from the University Paris Dauphine and a Ph.D. in Management Sciences from the University of Liège, Belgium. He has been a Full Professor of Applied Mathematics and Computer Science at the University of Luxembourg, where he taught courses on algorithmic decision theory, computational statistics and discrete mathematics. He has served the international OR community as President of the Belgian OR Society (ORBEL), Vice-President of the Association of European OR Societies (EURO) and Vice-President of the International Federation of OR Societies (IFORS). His main interest is in outranking-based decision aiding algorithms for selecting, ranking and rating with multiple incommensurable performance criteria. His major articles have appeared in the European Journal of Operational Research (EJOR), Computer & Operations Research, and the Journal of Multi-Criteria Decision Analysis (JMCDA).

Inhalt

Part I: Introduction to the DIGRAPH3 Python Resources.- 1. Working with the DIGRAPH3 Python Resources.- 2. Working with Bipolar-Valued Digraphs.- 3. Working with Outranking Digraphs.- Part II: Evaluation Models and Decision Algorithms.- 4. Building a Best Choice Recommendation.- 5. How to Create a New Multiple-Criteria Performance Tableau.- 6. Generating Random Performance Tableaux.- 7. Who Wins the Election?.- 8. Ranking with Multiple Incommensurable Criteria.- 9. Rating by Sorting into Relative Performance Quantiles.- 10. Rating-by-Ranking with Learned Performance Quantile Norms.- 11. HPC Ranking of Big Performance Tableaux.- Part III: Evaluation and Decision Case Studies.- 12. Alice's Best Choice: A Selection Case Study.- 13. The Best Academic Computer Science Depts: A Ranking Case Study.- 14. The Best Students, Where Do They Study? A Rating Case Study.- 15. Exercises.- Part IV: Advanced Topics.- 16. On Measuring the Fitness of a Multiple-Criteria Ranking.- 17. On Computing Digraph Kernels.- 18. On Confident Outrankings with Uncertain Criteria Significance Weights.- 19. Robustness Analysis of Outranking Digraphs.- 20. Tempering Plurality Tyranny Effects in Social Choice.- Part V: Working with Undirected Graphs.- 21. Bipolar-Valued Undirected Graphs.- 22. On Tree Graphs and Graph Forests.- 23. About Split, Comparability, Interval, and Permutation Graphs.