Publications du laboratoire
(51) Production(s) de RICO A.


Graded cubes of opposition and possibility theory with fuzzy events
Auteur(s): Dubois Didier, Prade Henri, Rico A.
(Article) Publié:
International Journal Of Approximate Reasoning, vol. p.168185 (2017)
Résumé: The paper discusses graded extensions of the cube of opposition, a structure that naturally emerges from the square of opposition in philosophical logic. These extensions of the cube of opposition agree with possibility theory and its four set functions. This extended cube then provides a synthetic and unified view of possibility theory. This is an opportunity to revisit basic notions of possibility theory, in particular regarding the handling of fuzzy events. It turns out that in possibility theory, two extensions of the four basic set functions to fuzzy events exist, which are needed for serving different purposes. The expressions of these extensions involve manyvalued conjunction and implication operators that are related either via semiduality or via residuation.



Organizing families of aggregation operators into a cube of opposition
Auteur(s): Dubois Didier, Prade Henri, Rico A.
Chapître d'ouvrage: Organizing Families Of Aggregation Operators Into A Cube Of Opposition, vol. p.2747 (2016)
Résumé: The cube of opposition is a structure that extends the traditional square of opposition originally introduced by Ancient Greek logicians in relation with the study of syllogisms. This structure that relates formal expressions has been recently generalized to non Boolean, graded statements. In this short paper, it is shown that the cube of opposition applies to wellknown families of idempotent, monotonically increasing aggregation operations, used in multiple criteria decision making, which qualitatively or quantitatively provide evaluations between the minimum and the maximum of the aggregated quantities. This covers weighted minimum and maximum, and more generally Sugeno integrals on the qualitative side, and Choquet integrals, with the important particular case of Ordered Weighted Averages, on the quantitative side. The interest of the cube of opposition is to display the various possible aggregation attitudes in a given setting and to show their complementarity.



An axiomatisation of discrete possibilistic Choquet integrals
Auteur(s): Dubois Didier, Rico A.
Conference: Foundations of Utility and Risk 2016 (FUR) (Warwick, GB, 20160627)
Résumé: Necessity (resp. possibility) measures are very simple representations of epistemic uncertainty due to incomplete knowledge. In the present work, a characterization of Choquet integral with respect to a possibility or a necessity measure is proposed, understood as a criterion for decision under uncertainty. This kind of criterion has the merit to be very simple to define and compute. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the decisionmaker preferences only reflect the plausibility ordering between states of nature.



Axiomatisation of discrete fuzzy integrals with respect to possibility and necessity measures
Auteur(s): Rico A.
Conference: 13th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2016) (Sant Julia de Loria, AD, 20160919)
Actes de conférence: Modeling Decisions for Artificial Intelligence, vol. p.pp. 94105 (2016)
Ref HAL: hal01445244_v1
Résumé: Necessity (resp. possibility) measures are very simple representations of epistemic uncertainty due to incomplete knowledge. In the present work, a characterization of discrete Choquet integrals with respect to a possibility or a necessity measure is proposed, understood as a criterion for decision under uncertainty. This kind of criterion has the merit of being very simple to define and compute. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the decisionmaker preferences only reflect the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an average of the maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The additional axiom can be also used in the axiomatic approach to Sugeno integral and generalized forms thereof. The possibility of axiomatising of these criteria for decision under uncertainty in the setting of preference relations among acts is also discussed.



Residuated variants of Sugeno integrals: Towards new weighting schemes for qualitative aggregation methods
Auteur(s): Dubois Didier, Prade Henri, Rico A.
(Article) Publié:
Information Sciences, vol. vol. 329 p.pp. 765781 (2016)
Ref HAL: hal01538305_v1
DOI: 10.1016/j.ins.2015.09.034
Résumé: Sugeno integrals and their particular cases such as weighted minimum and maximum have been used in multiplecriteria aggregation when the evaluation scale is qualitative. This paper proposes two new variants of weighted minimum and maximum, where the criteria weights play the role of tolerance thresholds. These variants require the use of a residuated structure, equipped with an involutive negation. We propose residuated counterparts of Sugeno integrals, where the weights bear on subsets of criteria, and we study their properties, showing they are analogous to Sugeno integrals to a large extent. Finally we propose dual aggregation operations, we call desintegrals, where an item is evaluated in terms of its defects rather than in terms of its positive features. Desintegrals are maximal when no defects at all are present, while integrals are maximal when all merits are sufficiently present. Qualitative integrals and desintegrals suggest a possible approach to bipolar evaluation processes where items are judged both in terms of merits and defects that are not independent of one another.



Generalized Sugeno Integrals
Auteur(s): Dubois Didier, Prade Henri, Rico A., Teheux Bruno
Conference: 16th International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems (IPMU 2016) (Eindhoven, NL, 20160620)
Actes de conférence: Information Processing and Management of Uncertainty in KnowledgeBased Systems, vol. II p.pp. 363374 (2016)
Ref HAL: hal01445233_v1
Résumé: Sugeno integrals are aggregation functions defined on a qualitative scale where only minimum, maximum and orderreversing maps are allowed. Recently, variants of Sugeno integrals based on Gödel implication and its contraposition were defined and axiomatized in the setting of bounded chain with an involutive negation. This paper proposes a more general approach. We consider totally ordered scales, multivalued conjunction operations not necessarily commutative, and implication operations induced from them by means of an involutive negation. In such a context, different Sugenolike integrals are defined and axiomatized.



Axiomatisation de l'intégrale de Choquet possibiliste
Auteur(s): Dubois Didier, Rico A.
Conference: Logique Floue et ses Applications (poitiers, FR, 20151105)
Actes de conférence: , vol. p. ()
Résumé: 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
