Abstract: In decision applications, especially multicriteria decision-making, numerical approaches are often questionable because it is hard to elicit numerical values quantifying preference, criteria importance or uncertainty. More often than not, multicriteria decision-making methods, especially fuzzy set based ones, come down to number-crunching recipes with debatable foundations.

In the first part of the tutorial we provide a critical assessment of some evaluation techniques based on fuzzy sets. We discuss
- the meaning of scales for membership functions and its consequence on aggregation operations,
- the cognitive limitations of numerical approaches to evaluation
- the use of linguistic variables, and fuzzy intervals.

In contrast, qualitative approaches where only maximum and minimum are used, enjoy a property of scale invariance that insures their robustness. One of the most sophisticated aggregation operation making sense on qualitative scales is Sugeno integral. It is not purely ordinal as it assumes commensurability between preference intensity and criteria importance or similarly, utility and uncertainty. We shall provide an introduction to qualitative decision theory under uncertainty based on possibility theory.

However, since absolute qualitative value scales must have few levels so as to remain cognitively plausible, there are as not more classes of equivalent decisions than value levels. We shall present results on the use of qualitative aggregation techniques, and the way of overcoming their main defect: the lack of discrimination power.

Qualitative aggregations such as Sugeno integrals cannot be strictly increasing and violate the strict Pareto property. In this tutorial, we report results obtained when trying to increase the discrimination power of Sugeno integrals, generalizing such refinements of the minimum and maximum as leximin and leximax. The representation of leximin and leximax by sums of numbers of different orders of magnitude (forming a super-increasing sequence) can be generalized to weighted max and min (yielding a "big-stepped" weighted average) and Sugeno integral (yielding a "big-stepped" Choquet integral). This methodology also requires qualitative monotonic set-functions to be refined by numerical set-functions, and we show they can always be belief or plausibility functions in the sense of Shafer.

Finally the last part of the tutorial will present results on bipolar qualitative approaches to multifactorial evaluations. While many evaluation methods aim at providing a preference ranking of decisions, not so many of them deal with the fact that an option can be intrinsically good or bad. We review bipolar qualitative decision rules and show they bridge the gap between decision heuristics based on focalisation on the most important criteria, and numerical bipolar approaches like cumulative prospect theory, and bicapacity methods.