Representations of Importance and Interaction of Fuzzy Measures, Capacities, Games and Its Extensions: A Survey

Abstract

Abstract. This paper gives a survey of the theory and results on representation of importance and interaction of fuzzy measures, capacities, games and its extensions: games on convex geometries, bi-capacities, bi-cooperative games, and multi-choice games, etc. All these games are regarded as games on products of distributive lattices or on regular set systems.

On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application

“…A whole theory on interacting criteria phenomena and on how to measure such phenomena is now well established (mainly) following the work by Murofushi and Soneda (1993), which was generalized by Grabisch (1996b), axiomatized by Grabisch and Roubens (1999), and also studied by other authors, as for example, Fujimoto (2010), Fujimoto et al (2006), Grabisch et al (2000), and Kojadinovic (2007b).…”

On the Robustness of the Sign of Nonadditivity Index in a Choquet Integral Model

“…It is well known that the interaction among criteria caused by the nonadditivity of a capacity can be measured by a cardinal probabilistic interaction index, in particular the Shapley interaction index 8,26 . More details in the literature on axiomatic properties of all kinds of cardinal probabilistic interaction indices can be found in 4,5,6,10 . Besides the Shapley interaction index 30 suggests to interpret this lack of compatibility with an additive model using the notion of nonadditivity, which is the subject of this paper.…”