## Topic outline

### General

- General news about the course
Forum whose main goal is to exchange and ask questions about the courses, the papers to be read for the evaluation, etc.

### Course content and evaluation

#### Content

This course will be in different modules, each of them introducing a particular aspect of decision theory. This year will be divided into two modules:

- Decision under uncertainty (S. Destercke, 12h)
- Multi-criteria decision-making, preferences and connected aspects (K. Belahcene, 12h)

#### Evaluation

As requested by UTC, we will perform two types of evaluations. The first one is an individual assignment, while the second is a group assignment.

**Exercice creation or "being in a TA shoes".**In this first assignment, each student should create one exercice in relation to the course (it can concern any part of the course, either on multi-objective/multi-criteria optimisation or on decision under uncertainty), that either emphasizes some aspect of the course, allows one to practice some of its aspects, or investigate a topic connected to the course, but that we did not explore. Each student would then be in the shoe of a teaching assistant (TA) in charge of producing exercices for practical/training classes or courses. What we expect as a result of this assignment is the following:

- The exercise statement, presenting the problem to be solved and the various associated questions and sub-questions (there can be only one main question/statement, or multiple follow-up questions).
- A detailed solution of the exercise (not just the end result), so that another TA (or ourselves) can reuse the exercise easily
- A short explanation (it can be a single paragraph or more) of the pedagogical purpose of the exercise: to practice some technical aspects, to illustrate a particular point, to make the student discover new concepts, etc... in short, after having done this exercise, what would be the gain of the student?
- Students are allowed to communicate/exhange ideas of exercises and even build them together. However, at the end, we expect EACH student to provide a different exercise (numerical variations of the same exercise will not be considered as different exercises).

**Paper illustration or "explain to your high-school nephew".**In this second assignment, each group (of maximum 3 people, minimum 1) will take a paper (a non-exhaustive and regularly updated list can be found at the end of the page) and will have the task to illustrate/explain a part of the paper through a media of their choice: it can be a presentation, a video, a poster, a live demonstration/exercise, an interactive website, etc. The rules are as follows:- The illustration/explanation should be pedagogical, in the sense that it should be accessible to a non-expert (that does not know advanced maths or computing). It should not be too long (i.e., less than 10/15 minutes).
- Depending on the size and complexity of the paper, not all of it has to be explained/illustrated. It is better to focus on a specific part and be really pedagogical/illustrative than trying to show too much and be confusing.
- If needed, students are encouraged to also look at connected papers to better understand their links.
- Each group must take a different paper. The rule is first come, first served (each time a group chooses a paper and tells us so, this paper is no longer available).

#### Lecturers

- Sébastien Destercke, Heudiasyc laboratory
- Khaled Belahcene, Heudiasyc laboratory

### Introductory notes

Lecture slides will be provided here, once they have been polished and corrected as much as we can. If you let us know if there is some error or typos remaining, we will be thankful.

This year course will be online, and each teacher will handle the situation to the best of its human capabilities. We ask the students to be understanding, and apologize for any (almost inevitable) decrease in pedagogical quality.

### Part 1: Decision under uncertainty

Materials concerning the part on decision under uncertainty

Lectures in this part are done by small (and not so small) modules, with a non-linear, tree-structured way to go through them. At the end of a module, the idea is that students can choose what topic will be covered next. This means some of them will be covered in class, others will not be, but most will be provided here. In addition, the provided course trees (given in the navigation .pdf files) will lead you, when those have been done, to videos allowing students to catch up with the materials, or to visit materials not covered in class.

### Part 2: Multi-criteria decision making

Materials concerning the part on Multi-criteria decision

### Part 3: Multi-objective optimisation

Materials concerning the part on multi-objective optimisation

### Non-exhaustive list of possible papers for the second assignment

Here is a list of possible papers. Hardness of a paper range from + (rather easy to follow) to +++++ (quite hard to follow) and is based on our subjective perception of the paper. We expect that the easier a paper is, the more of it is covered in the ilustration, and the more worked out this later is.

#### Selected papers

- Couso, I., Moral, S., & Walley, P. (2000). A survey of concepts of independence for imprecise probabilities.
*Risk, Decision and Policy*,*5*(2), 165-181.**Topic:**independence notions for imprecise probabilities**Nature:**survey paper**Hardness:**+++**Group:**and**El Hadj Mohamedou****Mohamed Ibrahim Attala** - Mauá, D. D., Conaty, D., Cozman, F. G., Poppenhaeger, K., & de Campos, C. P. (2018). Robustifying sum-product networks.
*International Journal of Approximate Reasoning*,*101*, 163-180.**Topic:**extending a specific probabilistic circuit (can be seen as a specific neural network) to deal with probability sets**Nature:**mostly methodological (some theory)**Hardness:**++++**Group:****Pascal Quach** - Troffaes, M. C. (2007). Decision making under uncertainty using imprecise probabilities.
*International journal of approximate reasoning*,*45*(1), 17-29.**Topic:**review of different decision rules using imprecise probabilities (including some not seen in class)**Nature:**survey paper**Hardness:**++/+++**Group: Maxime Delboulle** - Braziunas, D. & Boutilier, C. (2010). Assessing regret-based preference elicitation with the UTPref recommendation system.
*Proceedings of the 11th ACM Conference on Electronic Commerce, EC-2010*, pp. 219-228.**Topic:**proposing an approach based on regret to select queries allowing to efficiently elicit a preference model**Nature:**short technical introduction to the model + experimental assessment**Hardness:**++**Group: Gimelli Andrea and Karim Pedemont** **Zaffalon, M., Corani, G., & Mauá, D. (2012).**Evaluating credal classifiers by utility-discounted predictive accuracy.*International Journal of Approximate Reasoning*,*53*(8), 1282.

Nature: methodological

Hardness: +++**Group: Hugo Martin**and**Robin Monge****Tversky, A., & Kahneman, D. (1974).**Judgment under Uncertainty: Heuristics and Biases: Biases in judgments reveal some heuristics of thinking under uncertainty.*science*,*185*(4157), 1124-1131.

Topic: Judgment heuristics people are susceptible to when assessing uncertaintiesexperimental**Nature:**++**Hardness:****Group:****Gentjan Gjinalaj**and**Ermal Belul****Bouyssou, D., Marchant, T. & Pirlot, M. (2022).**A note on ELECTRE TRI-nB with few limiting profiles.*4OR*20(3): 443-463.**Topic:**relative positionning of stylized approaches to sorting**Nature:**overview of some sorting models, and detailed analysis of their relations**Hardness:**++/+++**Group: Besa Salimusaj , Alban Zyle**and**Ambra Zajsi****Greco, S., Matarazzo, B., and Slowinski, R. (1999).**Rough approximation of a preference relation by dominance relations.*European Journal of Operational Research*, 117:63–83.**Topic:**bridging the gap between numeric and symbolic approaches to handling preferences**Nature:**detailed and technical introduction to the model**Hardness:**++/+++**Group: Riccardo Gjini**and**Tommaso Parodi**

#### Part 1: decision and reasoning under uncertainty

- Dubois, D., Fargier, H., Prade, H., & Sabbadin, R. (2009). A survey of qualitative decision rules under uncertainty.
*Decision‐making Process: Concepts and Methods*, 435-473.**Topic:**decision theory with a qualitative perspective (no number at all), with a Savage-like justification**Nature:**theoretical**Hardness:**++++ - Bernard, J. M. (2005). An introduction to the imprecise Dirichlet model for multinomial data.
*International Journal of Approximate Reasoning*,*39*(2-3), 123-150.**Topic:**extending the Dirichlet model used in Bayesian approaches to estimate multinomials to the imprecise case**Nature:**detailed and technical introduction to the model**Hardness:**++/+++ - Hansen, P., Jaumard, B., De Aragao, M. P., Chauny, F., & Perron, S. (2000). Probabilistic satisfiability with imprecise probabilities.
*International Journal of Approximate Reasoning*,*24*(2-3), 171-189.**Topic:**Dealing with satisfiability in logic when probabilities are imprecise**Nature:**methodological paper with algorithms**Hardness:**+++ - Mauá, D. D., & Cozman, F. G. (2020). Thirty years of credal networks: Specification, algorithms and complexity.
*International Journal of Approximate Reasoning*,*126*, 133-157.**Topic:**Review on the use of graphical models (extensions of Bayesian networks) with imprecise probabilities**Nature:**survey paper**Hardness:**+++

#### Part 2: multi-criteria decision making and preferences

- Rolland, A. (2013). Reference-based preferences aggregation procedures in multi-criteria decision making.
*European Journal of Operational Research*, 225, 479–486.**Topic:**Introduces a model for noncompensatory ranking very close to XAI sparse linear models**Nature:**detailed and technical introduction to the model**Hardness:**++ - Labreuche C. & Grabisch M. (2018). Using multiple reference levels in Multi-Criteria Decision aid: The Generalized-Additive Independence model and the Choquet integral approaches.
*European Journal of Operational Research*, 267, 598–611.**Topic:**models that allow to go beyond the independence assumption underlying the additive value model**Nature:**detailed and technical introductions to the models**Hardness:**+++

- Fishburn, P. (1996). Finite Linear Qualitative Probability.
*Journal of mathematical psychology*, 40, 64-77**Topic:**characterization of additive set preferences**Nature:**highly technical analysis of the problem**Hardness:**++++

- Couso, I., Moral, S., & Walley, P. (2000). A survey of concepts of independence for imprecise probabilities.