In this paper, the cooperative games with fuzzy coalitions were discussed. Several integral representations which described the fuzzy character function of the cooperative game were given, and the important solution –-the Shapley function was also investigated. For the cooperative game where the rate of participation of every player in a coalition is allowed to range within interval [0,1], the ...

The additivity property of the ``measure'', one of the most important concepts in mathematics, is often inflexible or too rigid to represent the many facets of human reasoning. In order to be able to express human subjectivity, recent researches proposed to replace this property by a weaker one, the ``monotonicity'' and called these non-additive monotonic measures ``fuzzy measures''. “Fuzzy int...

The assertion in question comes from the short final section in the Theory of Capacities of Choquet 1953/54, in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this formation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and the counterpart with superadditive. His treatmen...

Choquet integral, as an adequate aggregation operator, extends the weighted mean operator by considering interactions among attributes. Choquet integral has been widely used in many real multi-attribute decision making. Weights (fuzzy measures) of attribute sets directly affect the decision results in multi-attribute decision making. In this paper, we aim to propose an objective method based on...

This paper is devoted to preference-based recommendation or configuration in the context of multiagent (or multicriteria) decision making. More precisely, we study the use of decomposable utility functions in the search for Choquet-optimal solutions on combinatorial domains. We consider problems where the alternatives (feasible solutions) are represented as elements of a product set of finite d...

The power of players in a collective decision process is a central issue in game theory. For this reason, the concept of influence of players on a simple game has been introduced. More generally, the influence of variables on Boolean functions has been defined and studied. We extend this concept to pseudo-Boolean functions, thus making it possible to appraise the degree of influence of any coal...

Given a probability measure over a state space, a partial collection (sub-σalgebra) of events whose probabilities are known, induces a capacity over the collection of all possible events. The induced capacity of an event F is the probability of the maximal (with respect to inclusion) event contained in F whose probability is known. The Choquet integral with respect to the induced capacity coinc...

Record linkage is used in data privacy to evaluate the disclosure risk of protected data. It models potential attacks, where an intruder attempts to link records from the protected data to the original data. In this paper we introduce a novel distance based record linkage, which uses the Choquet integral to compute the distance between records. We use a fuzzy measure to weight each subset of va...

The aim of this paper is to investigate the cone of non-negative, radial, positivedefinite functions in the set of continuous functions on R. Elements of this cone admit a Choquet integral representation in terms of the extremals. The main feature of this article is to characterize some large classes of such extremals. In particular, we show that there many other extremals than the gaussians, t...