We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations...

We study in this paper the notion of conditional relative importance in a quantitative framework. Bi-capacities are shown to be suitable to represent such notion. We restrict ourself to the case when the relative importance of two criteria are conditional on a third being attractive or...

In the paper, we introduce and study generalized weighted influence indices of a coalition on a player, where players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to influence of a coalition of other players, a final decision of the...

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of $[0,1]^n$. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their...

Set functions appear as a useful tool in many areas of decision making and operations research, and several linear invertible transformations have been introduced for set functions, such as the Möbius transform and the interaction transform. The present paper establish similar transforms and...

We are interested in modeling interaction between criteria in Multi-Criteria Decision Making when underlying scales are bipolar. Interacting phenomena involving behavioral bias between attractive and repulsive values are in particular considered here. We show in an example that both the Choquet...

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a...

Suppose that a decision maker provides a weak order on a given set of alternatives, each alternative being described by a vector of scores, which are given on a finite ordinal scale $E$. The paper addresses the question of the representation of this weak order by some mean operator, and gives...

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are...

In cooperative game theory, the Shapley value is a central notion defining a rational way to share the total worth of a game among players. In this paper, we address a general framework, namely regular set systems, where the set of feasible coalitions forms a poset where all maximal chains have...