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This paper presents a synthesis on the application of fuzzy integral as an innovative tool for criteria aggregation in decision problems. The main point is that fuzzy integrals are able to model interaction between criteria in a flexible way. The methodology has been elaborated mainly in Japan, and has been applied there successfully in various fields such… (More)

In the paper, we study a model of influence in a social network. It is assumed that each player has an inclination to say YES or NO which, due to influence of other players, may be different from the decision of the player. The point of departure here is the concept of the Hoede-Bakker index-the notion which computes the overall decisional 'power' of a… (More)

Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science,… (More)

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 better interpretation of the models and a better use of the… (More)

An axiomatization of the interaction between the players of any coalition is given. It is based on three axioms: linearity, dummy and symmetry. These interaction indices extend the Banzhaf and Shapley values when using in addition two equivalent recursive axioms. Lastly, we give an expression of the Banzhaf and Shapley interaction indices in terms of… (More)

This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation.

- Michel Grabisch, Sergei A. Orlovski, Ronald R. Yager

The problem of aggregating numerical values is addressed in this chapter. The first part deals with the aggregation of criteria into a single one. Properties which are suitable for this case are presented, together with the most common aggregation operators. A special section is devoted to ordered weighted averaging (OWA) operators, and fuzzy integrals.… (More)

This paper presents a synthesis of results on the concept of ¡-additive measures and the notion of representation of a fuzzy measure, since their introduction by the author in 1996. The collection of results will limit itself to results which are not connected with multicriteria decision making, since those are presented in a companion paper in this book,… (More)

- Michel GRABISCH
- 2004

We show that the Choquet integral is the unique linear interpolator between vertices of the [0, 1] n hyper-cube, using the least possible number of vertices. Related results by Lovász and Singer are discussed, as well as other interpolations. We show that the Choquet integral for bi-capacities can be also casted into this framework. Lastly, we discuss the… (More)