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


Extracting Decision Rules from Qualitative Data via Sugeno Utility Functionals
Auteur(s): Brabant Quentin, Couceiro Miguel, Dubois Didier, Prade Henri, Rico A.
(Document sans référence bibliographique) 20170000
Ref HAL: hal01670924_v1
Résumé: Sugeno integrals are qualitative aggregation functions. They are used in multiple criteria decision making and decision under uncertainty, for computing global evaluations of items, based on local evaluations. The combination of a Sugeno integral with unary order preserving functions on each criterion is called a Sugeno utility functionals (SUF). A noteworthy property of SUF is that they represent multithreshold decision rules, while Sugeno integrals represent singlethreshold ones. However, not all sets of multithreshold rules can be represented by a single SUF. In this paper, we consider functions defined as the minimum or the maximum of several SUF. These maxSUF and minSUF can represent all functions that can be described by a set of multithreshold rules, i.e., all orderpreserving functions on finite scales. We study their potential advantages as a compact representation of a big set of rules, as well as an intermediary step for extracting rules from empirical datasets.



Intégrales de Sugeno généralisées en analyse de données
Auteur(s): Couceiro Miguel, Dubois Didier, Prade Henri, Rico A.
Conference: LFA 2017  26èmes Rencontres Francophones sur la Logique Floue et ses Applications (Amiens, FR, 20171019)
Actes de conférence: , vol. p. (2017)
Ref HAL: hal01668232_v1
Résumé: Les intégrales de Sugeno permettent de décrire des familles d'opérateurs d'agrégation qualitativement. On sait que les intégrales de Sugeno peuvent être représentées par des ensembles de règles. Chaque règle utilise le même seuil dans les conditions et la conclusion. Cependant, en pratique on aimerait représenter des règles mettant en oeuvre plusieurs seuils. Certaines règles à plusieurs seuils peuvent se représenter par des "fonctionnelles d'utilité de Sugeno" où la valeur des critères peut être modifiéè a l'aide de fonctions d'utilité. Leur pouvoir de représentation reste assez restreint. Par contre, on suggère que l'usage de disjonctions ou de conjonctions de fonctionnelles d'utilité de Sugeno augmente de façon déterminante le pouvoir expressif et qu'on peut capturer ainsi toute fonction d'agrégation unaire par morceaux sur une échelle finie.



Enhancing the expressive power of Sugeno integrals for qualitative data analysis
Auteur(s): Couceiro Miguel, Dubois Didier, Prade Henri, Rico A.
Conference: Conference of the European Society for Fuzzy Logic and Technology IWIFSGN 2017, EUSFLAT 2017 (Warsaw, PL, 20170911)
Actes de conférence: International Workshop on Intuitionistic Fuzzy Sets and Generalized NetsProceedings of the Conference of the European Society for Fuzzy Logic and TechnologyIWIFSGN 2017, EUSFLAT 2017: Advances in Fuzzy Logic and Technology 2017, vol. 641 p.534547 (2017)
Ref HAL: hal01668229_v1
Résumé: Sugeno integrals are useful for describing families of multiple criteria aggregation functions qualitatively. It is known that Sugeno integrals, as aggregation functions, can be represented by a set of rules. Each rule refers to the same threshold in the conditions about the values of the criteria and in the conclusion pertaining to the value of the integral. However, in the general case we expect rules where several thresholds appear. Some of these rules involving different thresholds can be represented by Sugeno utility functionals where criteria values are rescaled by means of utility functions associated with each criterion. But as shown in this paper, their representation power is quite restrictive. In contrast, we provide evidence to conjecture that the use of disjunctions or conjunctions of Sugeno integrals with utility functions drastically improves the expressive power and that they can capture any aggregation function on a finite scale, understood as piecewise unary aggregation functions.



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.
