54 citations · 143 across the 34 of their papers we have counts for
6 papers · 1 filter
The Möbius transform on symmetric ordered structures and its application to capacities on finite sets
Michel Grabisch
Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure clos…
Axiomatic structure of k-additive capacities
Pedro Miranda, Michel Grabisch, Pedro Gil
In this paper we deal with the problem of axiomatizing the preference relations modelled through Choquet integral with respect to a -additive capacity, i.e. whose Möbius transfo…
Derivative of functions over lattices as a basis for the notion of interaction between attributes
Michel Grabisch, Christophe Labreuche
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of intera…
Bi-capacities -- Part I: definition, Möbius transform and interaction
Michel Grabisch, Christophe Labreuche
Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wi…
Bi-capacities -- Part II: the Choquet integral
Michel Grabisch, Christophe Labreuche
Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wi…
Entropy of capacities on lattices and set systems
Aoi Honda, Michel Grabisch
We propose a definition for the entropy of capacities defined on lattices. Classical capacities are monotone set functions and can be seen as a generalization of probability measur…