Choquet integral has proved to be an effective aggregation model in multiple criteria decision analysis when interactions between criteria have to be taken into consideration. Recently, some generalizations of Choquet integral have been proposed to take into account more complex forms of interaction. This is the case of the bipolar Choquet integral and of the level dependent Choquet integral. T...

In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can ...

The Choquet integral extended to negative functions can be defined in two ways, namley the asymmetric integral (usual Choquet integral) and the symmetric integral (also called the Šipoš integral). No such extension has been defined for the Sugeno integral. In this paper, after recalling the case of Choquet integral, we address the case of Sugeno integral, which we define in a purely ordinal fra...

The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov’s intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the emph{generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (GIVIFHGSCI) and the emph{interval-valued intuitionistic fuzzy Hamacher general...

This paper extends the Choquet integral, widely used in multi-attribute decision problems, to the non monotone case in the context of Group Decision Theory. Even if not so often, preference structures which violate the monotonicity axiom can be observed in real applications. Our aim is twofold. First, we propose the Choquet integral with non monotone non additive measure. Then, we apply the Cho...

We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable propertie...

Preference modeling consists in constructing a preference relation from initial preferences given by a decision maker. We are interested in the preference relation obtained from the use of the Choquet integral. The necessity preference is constructed as the intersection of all preference relations corresponding to a Choquet integral which are compatible with the initial preferences of the decis...

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 Choquet integral in multi-criteria decision ...

In the context of decision under uncertainty, we characterize the 2-additive Choquet integral on the set of fictitious acts called binary alternatives or binary actions. This characterization is based on a fundamental property called MOPI which permits us to relate belief functions and the 2additive Choquet integral. Keywords—Capacity, Möbius transform, Choquet integral, k-monotone function, Be...

In [Timonin, 2016] we developed a general axiomatic treatment of a popular multicriteria decision model the Choquet integral. This paper contains extensions of our results to the particular interesting special cases of the Choquet integral, analysis of some aspects of the Choquet integral model learning, and a discussion of the applications of our results in decision theory.