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See detailLa formule de Clark-Ocone et ses généralisations
Schiltz, Jang UL

Presentation (2000, December 13)

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See detailThe influence of variables on pseudo-Boolean functions with applications to game theory and multicriteria decision making
Marichal, Jean-Luc UL

in Discrete Applied Mathematics (2000), 107(1-3), 139-164

The power of players in a collective decision process is a central issue in game theory. For this reason, the concept of influence of players on a simple game has been introduced. More generally, the ... [more ▼]

The power of players in a collective decision process is a central issue in game theory. For this reason, the concept of influence of players on a simple game has been introduced. More generally, the influence of variables on Boolean functions has been defined and studied. We extend this concept to pseudo-Boolean functions, thus making it possible to appraise the degree of influence of any coalition of players in cooperative games. In the case of monotone games, we also point out the links with the concept of interaction among players. Although they do not have the same meaning at all, both influence and interaction functions coincide on singletons with the so-called Banzhaf power index. We also define the influence of variables on continuous extensions of pseudo-Boolean functions. In particular, the Lovász extension, also called discrete Choquet integral, is used in multicriteria decision making problems as an aggregation operator. In such problems, the degree of influence of decision criteria on the aggregation process can then be quite relevant information. We give the explicit form of this influence for the Choquet integral and its classical particular cases. [less ▲]

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See detailAn axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria
Marichal, Jean-Luc UL

in IEEE Transactions on Fuzzy Systems (2000), 8(6), 800-807

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute to ... [more ▼]

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute to the weighted arithmetic mean has to be adopted. We show that, under rather natural conditions, the discrete Choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by the taking into consideration of the interaction among criteria. The axiomatic that supports the Choquet integral is presented and an intuitive approach is proposed as well. [less ▲]

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See detailEntropy of discrete fuzzy measures
Marichal, Jean-Luc UL; Roubens, Marc

in International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems (2000), 8(6), 625-640

The concept of entropy of a discrete fuzzy measure has been recently introduced in two different ways. A first definition was proposed by Marichal in the aggregation framework, and a second one by Yager ... [more ▼]

The concept of entropy of a discrete fuzzy measure has been recently introduced in two different ways. A first definition was proposed by Marichal in the aggregation framework, and a second one by Yager in the framework of uncertain variables. We present a comparative study between these two proposals and point out their properties. We also propose a definition for the entropy of an ordinal fuzzy measure, that is, a fuzzy measure taking its values in an ordinal scale in the sense of measurement theory. [less ▲]

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See detailDifférentiation sur les espaces de Sobolev généralisés
Schiltz, Jang UL

Presentation (2000, November 25)

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See detailLe chaos de Wiener et l'intégrale de Skohorod
Schiltz, Jang UL

Presentation (2000, November 15)

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See detailOn perfect, amicable, and sociable chains
Marichal, Jean-Luc UL

E-print/Working paper (2000)

Let $\bfx = (x_0,\ldots,x_{n-1})$ be an $n$-chain, i.e., an $n$-tuple of non-negative integers $< n$. Consider the operator $s: \bfx \mapsto\bfx' = (x'_0,\ldots,x'_{n-1})$, where $x'_j$ represents the ... [more ▼]

Let $\bfx = (x_0,\ldots,x_{n-1})$ be an $n$-chain, i.e., an $n$-tuple of non-negative integers $< n$. Consider the operator $s: \bfx \mapsto\bfx' = (x'_0,\ldots,x'_{n-1})$, where $x'_j$ represents the number of $j$'s appearing among the components of $\bfx$. An $n$-chain $\bfx$ is said to be perfect if $s(\bfx) = \bfx$. For example, (2,1,2,0,0) is a perfect 5-chain. Analogously to the theory of perfect, amicable, and sociable numbers, one can define from the operator $s$ the concepts of amicable pair and sociable group of chains. In this paper we give an exhaustive list of all the perfect, amicable, and sociable chains. [less ▲]

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See detailOn the associativity functional equation
Marichal, Jean-Luc UL

in Fuzzy Sets & Systems (2000), 114(3), 381-389

Let [a,b] be any bounded closed real interval. The class of all continuous, nondecreasing, associative functions M : [a,b]^2 --> [a,b] fulfilling the boundary conditions M(a,a)=a and M(b,b)=b is described.

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See detailOn Sugeno integral as an aggregation function
Marichal, Jean-Luc UL

in Fuzzy Sets & Systems (2000), 114(3), 347-365

The Sugeno integral, for a given fuzzy measure, is studied under the viewpoint of aggregation. In particular, we give some equivalent expressions of it. We also give an axiomatic characterization of the ... [more ▼]

The Sugeno integral, for a given fuzzy measure, is studied under the viewpoint of aggregation. In particular, we give some equivalent expressions of it. We also give an axiomatic characterization of the class of all the Sugeno integrals. Some particular subclasses, such as the weighted maximum and minimum functions are investigated as well. [less ▲]

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See detailInfluence de l'expression émotionnelle de l'einseignant sur l'agressivité des élèves
Steffgen, Georges UL

Scientific Conference (2000, September)

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See detailEindrucksbildung aus Personbeschreibungen: Syntaktische Kohärenz und soziale Informationsverarbeitung.
Krolak-Schwerdt, Sabine UL; Wintermantel, Margret

Scientific Conference (2000, September)

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See detailMentale Modelle beim Verstehen von Personbeschreibungen: Konsistenz der Information und Kohärenz des Textes.
Wintermantel, Margret; Krolak-Schwerdt, Sabine UL

Scientific Conference (2000, September)

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See detailDetermination of weights of interacting criteria from a reference set
Marichal, Jean-Luc UL; Roubens, Marc

in European Journal of Operational Research (2000), 124(3), 641-650

In this paper, we present a model allowing to determine the weights related to interacting criteria. This is done on the basis of the knowledge of a partial ranking over a reference set of alternatives ... [more ▼]

In this paper, we present a model allowing to determine the weights related to interacting criteria. This is done on the basis of the knowledge of a partial ranking over a reference set of alternatives (prototypes), a partial ranking over the set of criteria, and a partial ranking over the set of interactions between pairs of criteria. [less ▲]

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See detailSteigert Selbstvertrauen die Leistung beim Bewegungslernen
Bund, Andreas UL

in dvs-Informationen (2000), 15

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See detailThe Sectio Aurea in a Fugue by Darius Milhaud
Anders-Malvetti, Ursula UL

Presentation (2000, July 17)

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See detailOn the entropy of non-additive weights
Marichal, Jean-Luc UL; Roubens, Marc

Scientific Conference (2000, July)

We consider a Choquet capacity, that is a set function which describes the importance of every subset of criteria in a MCDA problem. The following question is approached: what is the generalized ... [more ▼]

We consider a Choquet capacity, that is a set function which describes the importance of every subset of criteria in a MCDA problem. The following question is approached: what is the generalized counterpart of the Shannon entropy (defined for a probabilistic measure) for such a capacity? The extension that is proposed depends on the scale type. In the cardinal case, the entropy is defined in terms of the first derivatives of the non-additive measures. In the ordinal case, it refers to the cardinality of the scale values that appear in the set of all capacities. Both generalized entropies are symmetric functions of the capacities and their extreme values (max entropy and min entropy) are characterized. An application to the determination of weights is given when interacting criteria are considered. [less ▲]

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See detailAdaptability in strategy choice: example of Blocks Designs task
Houssemand, Claude UL

Scientific Conference (2000, July)

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See detailTranscriptional modulation of the anti-apoptotic protein BCL-XL by the paired box transcription factors PAX3 and PAX3/FKHR
Margue, Christiane UL; Bernasconi, Michele; Barr, Frederik et al

in Oncogene (2000), 19(25), 2921

The aberrant expression of the transcription factors PAX3 and PAX3/FKHR associated with rhabdomyosarcoma (RMS), solid tumors displaying muscle cell features, suggests that these proteins play an important ... [more ▼]

The aberrant expression of the transcription factors PAX3 and PAX3/FKHR associated with rhabdomyosarcoma (RMS), solid tumors displaying muscle cell features, suggests that these proteins play an important role in the pathogenesis of RMS. We could previously demonstrate that one of the oncogenic functions of PAX3 and PAX3/FKHR in RMS is protection from apoptosis. BCL-XL is a prominent anti-apoptotic protein present in normal skeletal muscle and RMS cells. In the present study, we establish that BCL-XL is transcriptionally modulated by PAX3 and PAX3/FKHR, since enhanced expression of both PAX proteins stimulates transcription of endogenous BCL-XL mRNA in a cell type specific manner. Further, we present evidence that both PAX3 and PAX3/FKHR can transcriptionally activate the Bcl-x gene promoter in cotransfection assays. Using electrophoretic mobility shift assays, an ATTA binding site for PAX3 and PAX3/FKHR could be localized in the upstream promoter region (position -42 to -39). Finally, ectopic overexpression of either PAX3, PAX3/FKHR or BCL-XL can rescue tumor cells from apoptosis induced by antisense treatment. These results suggest that at least part of the anti-apoptotic effect of PAX3 and PAX3/FKHR is mediated through direct transcriptional modulation of the prominent anti-apoptotic protein BCL-XL. [less ▲]

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