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)
There is given a short overview of the monograph " Aggregation Functions " (M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap), Cambridge University Press (in press) with more details from introductory Chapters 1 and 2.
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)
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.
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)
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)
This chapter aims at a unified presentation of various methods of MCDA based on fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet and Sugeno integral. A first section sets the position of the problem of multicriteria decision making, and describes the various possible scales of measurement (cardinal unipolar and bipolar, and ordinal).… (More)
The problem of combining pieces of information issued from several sources can be encountered in various fields of application. This paper aims at presenting the different aspects of information fusion in different domains, such as databases, regulations, preferences , sensor fusion, etc., at a quite general level. We first present different types of… (More)
In this paper, we introduce the Choquet integral as a general tool for dealing with multiple criteria decision making. After a theoretical exposition giving the fundamental basis of the methodology, practical problems are addressed, in particular the problem of determining the fuzzy measure. We give an example of application, with two different approaches,… (More)