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2 Operations Research and Decisions

2 2016

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Determining models of influence

Grabisch M., Rusinowska A.

Operations Research and Decisions

2016

Vol. 26, No. 2

69--85

We consider a model of opinion formation based on aggregation functions. Each player modifies his opinion by arbitrarily aggregating the current opinion of all players. A player is influential on another player if the opinion of the first one matters to the latter. Generalization of an influential player to a coalition whose opinion matters to a player is called an influential coalition. Influential players (coalitions) can be graphically represented by the graph (hypergraph) of influence, and convergence analysis is based on properties of the hypergraphs of influence. In the paper, we focus on the practical issues of applicability of the model w.r.t. a standard framework for opinion formation driven by Markov chain theory. For a qualitative analysis of convergence, knowing the aggregation functions of the players is not required, one only needs to know the set of influential coalitions for each player. We propose simple algorithms that permit us to fully determine the influential coalitions. We distinguish three cases: a symmetric decomposable model, an anonymous model, and a general model.

Choquet integral calculus on a continuous support and its applications

Ridaoui M., Grabisch M.

Operations Research and Decisions

2016

Vol. 26, No. 1

73--93

The results of the calculation of the Choquet integral of a monotone function on the nonnegative real line have been described. Next, the authors prepresented Choquet integral of nonmonotone functions, by constructing monotone functions from nonmonotone ones by using the increasing or decreasing rearrangement of a nonmonotone function. Finally, this paper considers some applications of these results to the continuous agregation operator OWA, and to the representation of risk measures by Choquet integral.