نتایج جستجو برای: Choquet finite integral

تعداد نتایج: 367271  

2009
Ulrich Faigle Michel Grabisch

In works dealing with capacities (fuzzy measures) and the Choquet integral on finite spaces, it is usually considered that all subsets of the universe are measureable. Hence, all functions are integrable in the sense of Choquet. We consider the situation where some subsets are not measurable (not feasible), so that there are nonintegrable functions. Since this is a severe limitation in applicat...

Journal: :Information Sciences 2022

We introduce a Choquet-Sugeno-like operator generalizing many operators for bounded nonnegative functions and monotone measures from the literature, e.g., Sugeno-like operator, Lovász Owen measure extensions, F-decomposition integral with respect to partition decomposition system, others. The new is based on concepts of dependence relation conditional aggregation operators, but it does not depe...

Journal: :Fuzzy Sets and Systems 2011
Ulrich Faigle Michel Grabisch

A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical nonnegative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on ...

2009
Ulrich FAIGLE Michel GRABISCH

We consider a collection F of subsets of a finite set N together with a capacity v : F → R+ and call a function f : N → R measurable if its level sets belong to F . Only in this case, the classical definition of the Choquet integral works in our wider context. In this article, we provide a general framework for a Choquet integral that works also for non-measurable functions f and includes the i...

2009
Silvia Angilella Salvatore Greco Benedetto Matarazzo

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...

Journal: :CoRR 2008
Michel Grabisch Christophe Labreuche

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of [0, 1]. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy. A second aim of the paper is to define a general mechanism...

Journal: :Kybernetika 2004
Yasuo Narukawa Vicenç Torra

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 ...

2000
Michel GRABISCH

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...

P. Kakati S. Borkotokey

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...

2003
Michel Grabisch Christophe Labreuche

We propose a general notion of capacity defined on any finite distributive lattice, encompassing usual capacities, bi-capacities, and their immediate extensions called k-ary capacities. We define key notions such as Möbius transform, derivative, Shapley value and Choquet integral.

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