DECision and COmplexity Axis  Publications
DECCO
(129) Production(s)


Comparison of two topological approaches for dealing with noisy labeling
Author(s): Rico F., Muhlenbach Fabrice, Zighed D. A., Lallich S.
(Article) Published:
Neurocomputing, vol. 160 p.3  17 (2015)
Ref HAL: hal01524431_v1
DOI: 10.1016/j.neucom.2014.10.087
Exporter : BibTex  endNote
Abstract: This paper focuses on the detection of likely mislabeled instances in a learning dataset. In order to detect potentially mislabeled samples, two solutions are considered which are both based on the same framework of topological graphs. The first is a statistical approach based on Cut Edges Weighted statistics (CEW) in the neighborhood graph. The second solution is a Relaxation Technique (RT) that optimizes a local criterion in the neighborhood graph. The evaluations by ROC curves show good results since almost 90% of the mislabeled instances are retrieved for a cost of less than 20% of false positive. The removal of samples detected as mislabeled by our approaches generally leads to an improvement of the performances of classical machine learning algorithms.



Axiomatisation de l'intégrale de Choquet possibiliste
Author(s): Dubois Didier, Rico A.
Conference: Logique Floue et ses Applications (poitiers, FR, 20151105)
Proceedings: , vol. p. ()
Abstract: A characterization of Choquet integral with respect to a possibility or a n\'ecessity measure is proposed. It is shown that it is enough to add a pessimism or an optimism axiom to the axioms of Choquet integral with respect to a capacity. This additional axiom enlarges the classes of functions in which Choquet integral is additive. The obtained pessimistic (resp. optimistic) criterion is an average of the maximin (resp. maximax) criterion of Wald across cuts of the possibility distribution. An axiomatisation of these criteria for decision under uncertainty is proposed in the setting of preference relations among acts



The Cube of Opposition and the Complete Appraisal of Situations by Means of Sugeno Integrals
Author(s): Dubois Didier, Prade Henri, Rico A.
Conference: 22nd International Symposium on Methodologies for Intelligent Systems (ISMIS 2015) (Lyon, FR, 20151021)
Proceedings: Foundations of Intelligent Systems 22nd International Symposium, ISMIS 2015, Lyon, France, October 2123, 2015, Proceedings, vol. p.197207 (2015)
Ref HAL: hal01291624_v1
Exporter : BibTex  endNote
Abstract: The cube of opposition is a logical structure that underlies many information representation settings. When applied to multiple criteria decision, it displays various possible aggregation attitudes. Situations are usually assessed by combinations of properties they satisfy, but also by combinations of properties they do not satisfy. The cube of opposition applies to qualitative evaluation when criteria are weighted as well as in the general case where any subset of criteria may be weighted for expressing synergies between them, as for Sugeno integrals. Sugeno integrals are wellknown as a powerful qualitative aggregation tool which takes into account positive synergies between properties. When there are negative synergies between properties we can use the socalled desintegral associated to the Sugeno integral. The paper investigates the use of the cube of opposition and of the ifthen rules extracted from these integrals and desintegrals in order to better describe acceptable situations.



Capacités qualitatives et information incomplète
Author(s): Dubois Didier, Prade Henri, Rico A.
(Article) Published:
Revue D'intelligence Artificielle (Revue Des Sciences Et Technologies De L'information), vol. vol. 29 p.pp. 493514 (2015)
Ref HAL: hal01290117_v1
DOI: 10.3166/RIA.29.493514
Exporter : BibTex  endNote
Abstract: Cet article étudie les capacités qualitatives, qui sont des fonctions d'ensemble monotones croissantes à valeurs sur un ensemble totalement ordonné muni d'une fonction de renversement de l'ordre. En nous inspirant du rôle joué par les probabilités pour les capacités quantitatives, nous cherchons à savoir si les capacités qualitatives peuvent être considérées comme des ensembles de mesures de possibilité. Plus précisément nous montrons que toute capacité qualitative est caracterisée par une classe de mesures de possibilité. De plus, les bornes inférieures de cette classe sont suffisantes pour reconstruire la capacité et leur nombre caractérise sa complexité. Nous présentons aussi un axiome généralisant la maxitivité des mesures de possibilité qui revient à préciser le nombre de mesures de possibilité nécessaires à la reconstruction de la capacité. Cet axiome nous permet aussi d'établir un lien entre capacité qualitative et logique modale non regulière. Enfin nous donnons quelques résultats pour caractériser la quantité d'information contenue dans une capacité.



The Cube of Opposition: A Structure Underlying Many Knowledge Representation Formalisms
Author(s): Dubois Didier, Prade Henri, Rico A.
Conference: IJCAI (Buenos Aires, AR, 20150725)
Proceedings: , vol. p. ()
Ref HAL: hal01192705_v1
Exporter : BibTex  endNote
Abstract: The square of opposition is a structure involving two involutive negations and relating quantified statements, invented in Aristotle time. Rediscovered in the second half of the XX th century,and advocated as being of interest for understanding conceptual structures and solving problems inparaconsistent logics, the square of opposition hasbeen recently completed into a cube, which corresponds to the introduction of a third negation.Such a cube can be encountered in very different knowledge representation formalisms, such asmodal logic, possibility theory in its allornothingversion, formal concept analysis, rough set theoryand abstract argumentation. After restating theseresults in a unified perspective, the paper proposes agraded extension of the cube and shows that severalqualitative, as well as quantitative formalisms, suchas Sugeno integrals used in multiple criteria aggregation and qualitative decision theory, or yet belieffunctions and Choquet integrals, are amenable totransformations that form graded cubes of opposition. This discovery leads to a new perspective onmany knowledge representation formalisms, layingtheir underlying common features. The cube of opposition exhibits fruitful parallelisms between different formalisms, which leads to highlight somemissing components present in one formalism andcurrently absent from another.



Le cube des oppositions  Une structure à la base de nombreux formalismes de représentation des connaissances
Author(s): Dubois Didier, Prade Henri, Rico A.
Conference: IAF (Rennes, FR, 20150629)
Ref HAL: hal01179578_v1
Exporter : BibTex  endNote
Abstract: The square of opposition is a structure involving two involutive negations and relating quantified statements, invented in Aristotle time. Rediscovered in the second half of the $XX^{th}$ century, and advocated as being of interest for understanding conceptual structures and solving problems in paraconsistent logics, the square of opposition has been recently completed into a cube, which corresponds to the introduction of a third negation. Such a cube can be encountered in very different knowledge representation formalisms, such as modal logic, possibility theory in its allornothing version, formal concept analysis, rough set theory and abstract argumentation. After restating these results in a unified perspective, the paper proposes a graded extension of the cube and shows that several qualitative, as well as quantitative formalisms, such as Sugeno integrals used in multiple criteria aggregation and qualitative decision theory, or yet belief functions and Choquet integrals, are amenable to transformations that form graded cubes of opposition. This discovery leads to a new perspective on many knowledge representation formalisms, laying their underlying common features. The cube of opposition exhibits fruitful parallelisms between different formalisms, which leads to highlight some missing components present in one formalism and currently absent from another.\end{abstract}



Extracting Decision Rules from Qualitative Data Using Sugeno Integral: A CaseStudy
Author(s): Dubois Didier, Durrieu Claude, Prade Henri, Rico A., Ferro Yannis
Conference: ECSQARU 2015 (compiègne, FR, 20150715)
Proceedings: , vol. p.1424 ()
Ref HAL: hal01179575_v1
Exporter : BibTex  endNote
Abstract: This paper deals with knowledge extraction from experimental data in multifactorial evaluation using Sugeno integrals. They are qualitative criteria aggregations where it is possible to assign weights to groups of criteria. A method for deriving such weights from data is recalled. We also present results in the logical representation of Sugeno integrals. Then we show how to extract ifthen rules expressing the selection of good situations on the basis of local evaluations, and rules to detect bad situations. We illustrate such methods on a casestudy in the area of water ecosystem health.
