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A complete description of comparison meaningful functions Marichal, Jean-Luc Presentation (2005, January 21) Detailed reference viewed: 62 (0 UL)k-intolerant capacities and Choquet integrals Marichal, Jean-Luc in Barthélemy, Jean-Pierre; Lenca, Philippe (Eds.) Advances in Multicriteria Decision Aid - Progrès en Aide Multicritère à la Décision (ENST Bretagne, 2005) (2005) We define an aggregation function to be (at most) k-intolerant if it is bounded from above by its kth lowest input value. Applying this definition to the discrete Choquet integral and its underlying ... [more ▼] We define an aggregation function to be (at most) k-intolerant if it is bounded from above by its kth lowest input value. Applying this definition to the discrete Choquet integral and its underlying capacity, we introduce the concept of k-intolerant capacities which, when varying k from 1 to n, cover all the possible capacities on n objects. Just as the concepts of k-additive capacities and p-symmetric capacities have been previously introduced essentially to overcome the problem of computational complexity of capacities, k-intolerant capacities are proposed here for the same purpose but also for dealing with intolerant or tolerant behaviors of aggregation. We also introduce axiomatically indices to appraise the extent to which a given capacity is k-intolerant and we apply them on a particular recruiting problem. [less ▲] Detailed reference viewed: 93 (9 UL)A complete description of comparison meaningful functions Marichal, Jean-Luc Presentation (2004, November 30) Comparison meaningful functions acting on some real interval are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful ... [more ▼] Comparison meaningful functions acting on some real interval are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful functions is further specified. Several already known results for comparison meaningful functions and invariant functions are obtained as consequences of our description. [less ▲] Detailed reference viewed: 122 (2 UL)Agrégation sur des échelles ordinales finies par des fonctions indépendantes des échelles Marichal, Jean-Luc ; in Actes des "Rencontres francophones sur la logique floue et ses applications" (LFA 2004), Nantes, France, Nov. 18-19, 2004 (2004, November) We give an interpretation of order invariant functions as scale independent functions for the aggregation on finite ordinal scales. More precisely, we show how order invariant functions can act, through ... [more ▼] We give an interpretation of order invariant functions as scale independent functions for the aggregation on finite ordinal scales. More precisely, we show how order invariant functions can act, through discrete representatives, on ordinal scales represented by finite chains. In particular, this interpretation allows us to justify the continuity property for certain order invariant functions in a natural way. [less ▲] Detailed reference viewed: 41 (0 UL)A complete description of comparison meaningful functions Marichal, Jean-Luc ; ; in Bouyssou, Denis; Janowitz, Mel; Roberts, Fred (Eds.) et al Annales du LAMSADE No 3 - Octobre 2004 (2004, October) Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful ... [more ▼] Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful functions is further specified. Several already known results for comparison meaningful functions and invariant functions are obtained as consequences of our description. [less ▲] Detailed reference viewed: 59 (3 UL)k-intolerant bi-capacities and veto criteria ; ; Marichal, Jean-Luc et al in López-Díaz, Miguel Concepcion; Gil, Maria Angeles; Grzegorzewski, Przemyslaw (Eds.) et al Soft Methodology and Random Information Systems (2004, July 30) We present the notion of k-intolerant bi-capacity, extending to the case of bipolar scales the notion of k-intolerant capacity recently proposed by Marichal. In a second part, we extend to the bipolar ... [more ▼] We present the notion of k-intolerant bi-capacity, extending to the case of bipolar scales the notion of k-intolerant capacity recently proposed by Marichal. In a second part, we extend to the bipolar case the notion of veto criteria. [less ▲] Detailed reference viewed: 117 (0 UL)Aggregation on finite ordinal scales by scale independent functions Marichal, Jean-Luc ; in Proc. 10th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004), Perugia, Italy, July 4-9, 2004 (2004, July) We give an interpretation of order invariant functions as scale independent functions for the aggregation on finite ordinal scales. More precisely, we show how order invariant functions can act, through ... [more ▼] We give an interpretation of order invariant functions as scale independent functions for the aggregation on finite ordinal scales. More precisely, we show how order invariant functions can act, through discrete representatives, on ordinal scales represented by finite chains. In particular, this interpretation allows us to justify the continuity property for certain order invariant functions in a natural way. [less ▲] Detailed reference viewed: 71 (0 UL)Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices ; ; Marichal, Jean-Luc in Proc. 10th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004), Perugia, Italy, July 4-9, 2004 (2004, July) In the framework of cooperative game theory and multicriteria decision making, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to ... [more ▼] In the framework of cooperative game theory and multicriteria decision making, the concept of interaction index, which can be regarded as an extension of that of value, has been recently proposed to measure the interaction phenomena among players or criteria. Axiomatizations of two classes of interaction indices, namely probabilistic interaction indices and cardinal-probabilistic interaction indices, generalizing probabilistic values and semivalues, respectively, are first proposed. Three existing instances of cardinal-probabilistic interaction indices encountered thus far in the literature are also axiomatized. [less ▲] Detailed reference viewed: 96 (1 UL)k-intolerant capacities and Choquet integrals Marichal, Jean-Luc in Proc. 10th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004), Perugia, Italy, July 4-9, 2004 (2004, July) We define an aggregation function to be (at most) k-intolerant if it is bounded from above by its kth lowest input value. Applying this definition to the discrete Choquet integral and its underlying ... [more ▼] We define an aggregation function to be (at most) k-intolerant if it is bounded from above by its kth lowest input value. Applying this definition to the discrete Choquet integral and its underlying capacity, we introduce the concept of k-intolerant capacities which, when varying k from 1 to n, cover all the possible capacities on n objects. Just as the concepts of k-additive capacities and p-symmetric capacities have been previously introduced essentially to overcome the problem of computational complexity of capacities, k-intolerant capacities are proposed here for the same purpose but also for dealing with intolerant or tolerant behaviors of aggregation. We also introduce axiomatically indices to appraise the extent to which a given capacity is k-intolerant. [less ▲] Detailed reference viewed: 80 (0 UL)Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral Marichal, Jean-Luc in European Journal of Operational Research (2004), 155(3), 771-791 In many multi-criteria decision-making problems the decision criteria present some interaction whose nature may vary from one situation to another. For example, some criteria may be statistically ... [more ▼] In many multi-criteria decision-making problems the decision criteria present some interaction whose nature may vary from one situation to another. For example, some criteria may be statistically correlated, thus making them somewhat redundant or opposed. Some others may be somewhat substitutive or complementary depending on the behavior of the decision maker. Some others may be decisive in the sense that the global score (of any alternative) obtained by aggregation is bounded by the partial score along one of them. In this paper we analyze this latter form of interaction. When a criterion bounds the global score from above, it is called a blocker or a veto, due to its rather intolerant character. When it bounds the global score from below, it is then called a pusher or a favor. We thus investigate the tolerance of criteria, or equivalently, the tolerance of the weighted aggregation operator (here the Choquet integral) that is used to aggregate criteria. More specifically, we propose (axiomatically) indices to appraise the extent to which each criterion behaves like a veto or a favor in the aggregation by the Choquet integral. Previous to this, we also propose global tolerance degrees measuring the extent to which the Choquet integral is conjunctive or disjunctive. [less ▲] Detailed reference viewed: 76 (2 UL)Aggregation on finite ordinal scales by scale independent functions Marichal, Jean-Luc ; in Order : A Journal on the Theory of Ordered Sets and its Applications (2004), 21(2), 155-180 We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have ... [more ▼] We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have discrete representatives when the ordinal scales are considered as totally ordered finite sets. We also show that those scale independent functions identify with the so-called order invariant functions, which have been described recently. In particular, this identification allows us to justify the continuity property for certain order invariant functions in a natural way. [less ▲] Detailed reference viewed: 78 (0 UL)An introduction to the PROSPER package for LaTeX users Marichal, Jean-Luc ; Schiltz, Jang Presentation (2004, March 09) PROSPER is a LaTeX class for writing transparencies. It is written on top of the seminar class by Timothy Van Zandt. It aims at offering an environment for easily creating slides for both presentations ... [more ▼] PROSPER is a LaTeX class for writing transparencies. It is written on top of the seminar class by Timothy Van Zandt. It aims at offering an environment for easily creating slides for both presentations with an overhead projector and a video projector. Slides prepared for a presentation with a computer and a video projector may integrate animation effects, incremental display, and such. [less ▲] Detailed reference viewed: 50 (5 UL)k-intolerant capacities and Choquet integrals Marichal, Jean-Luc in Klement, Erich Peter; Pap, Endre (Eds.) Proc. 25th Linz Seminar on Fuzzy Set Theory (LINZ 2004): Mathematics of Fuzzy Systems (2004, February) We define an aggregation function to be (at most) k-intolerant if it is bounded from above by its kth lowest input value. Applying this definition to the discrete Choquet integral and its underlying ... [more ▼] We define an aggregation function to be (at most) k-intolerant if it is bounded from above by its kth lowest input value. Applying this definition to the discrete Choquet integral and its underlying capacity, we introduce the concept of k-intolerant capacities which, when varying k from 1 to n, cover all the possible capacities on n objects. Just as the concepts of k-additive capacities and p-symmetric capacities have been previously introduced essentially to overcome the problem of computational complexity of capacities, k-intolerant capacities are proposed here for the same purpose but also for dealing with intolerant or tolerant behaviors of aggregation. [less ▲] Detailed reference viewed: 87 (1 UL)TOMASO, A solution in the presence of interacting points of views ; ; Marichal, Jean-Luc Article for general public (2004) This short article briefly presents the main features of the multiple criteria sorting tool TOMASO (Technique for Ordinal Multi-Attribute Sorting and Ordering) and its implementation. Its main ... [more ▼] This short article briefly presents the main features of the multiple criteria sorting tool TOMASO (Technique for Ordinal Multi-Attribute Sorting and Ordering) and its implementation. Its main particularities are the possibility to consider interacting points of view and the use of the Choquet integral as a discriminant function. The capacities are learnt through the use of protoypes, which are well known alternatives for the Decision Maker. [less ▲] Detailed reference viewed: 39 (1 UL)Derivative relationships between volume and surface area of compact regions in Rd Marichal, Jean-Luc Presentation (2003, October 21) We explore the idea that the derivative of the volume, V , of a region in Rp with respect to r equals its surface area, A, where r = p V/A. We show that the families of regions for which this formula for ... [more ▼] We explore the idea that the derivative of the volume, V , of a region in Rp with respect to r equals its surface area, A, where r = p V/A. We show that the families of regions for which this formula for r is valid, which we call homogeneous families, include all the families of similar regions. We determine equivalent conditions for a family to be homogeneous, provide examples of homogeneous families made up of non-similar regions, and offer a geometric interpretation of r in a few cases. [less ▲] Detailed reference viewed: 69 (1 UL)Aggregation on finite ordinal scales (Tutorial) Marichal, Jean-Luc in Proc. 2nd Int. Summer School on Aggregation Operators and their Applications (AGOP 2003), Alcalá de Henares (Madrid), Spain, July 14-18, 2003 (2003, July) We give an interpretation of order invariant functions as scale independent functions for the aggregation on ¯nite ordinal scales. More precisely, we show how order invariant functions can act, through ... [more ▼] We give an interpretation of order invariant functions as scale independent functions for the aggregation on ¯nite ordinal scales. More precisely, we show how order invariant functions can act, through discrete representatives, on ordinal scales represented by finite chains. In particular, this interpretation allows us to justify the continuity property for certain order invariant functions in a natural way. [less ▲] Detailed reference viewed: 51 (2 UL)On tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral Marichal, Jean-Luc in Bisdorff, Raymond (Ed.) Proc. 14th Mini-Euro Conference, Human Centered Processes, Distributed Decision Making and Man-Machine Cooperation (HCP 2003), Luxembourg, May 5-7, 2003 (2003, May) In many multi-criteria decision making problems the criteria present some interaction whose nature may vary from one situation to another. When a criterion bounds the global score from above, it is called ... [more ▼] In many multi-criteria decision making problems the criteria present some interaction whose nature may vary from one situation to another. When a criterion bounds the global score from above, it is called a veto, due to its rather intolerant character. When it bounds the global score from below, it is then called a favor. In this paper we investigate the tolerance of criteria, or equivalently, the tolerance of the weighted aggregation operator (here the Choquet integral) which is used to aggregate criteria. More specifically, we propose (axiomatically) indices to appraise the extent to which each criterion behaves like a veto or a favor in the aggregation by the Choquet integral. [less ▲] Detailed reference viewed: 71 (0 UL)On order invariant synthesizing functions Marichal, Jean-Luc in Journal of Mathematical Psychology (2002), 46(6), 661-676 This paper gives a description of the class of continuous functions that are comparison meaningful in the sense of measurement theory. When idempotency is assumed, this class reduces to the Boolean max ... [more ▼] This paper gives a description of the class of continuous functions that are comparison meaningful in the sense of measurement theory. When idempotency is assumed, this class reduces to the Boolean max-min functions (lattice polynomials). In that case, continuity can be replaced by increasing monotonicity, provided the range of variables is open. The particular cases of order statistics and projection functions are also studied. [less ▲] Detailed reference viewed: 88 (1 UL)On order invariant synthesizing functions Marichal, Jean-Luc in Proc. 9th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2002), Annecy, France, July 1-5, 2002 (2002, July) We give a description of the class of continuous functions that are comparison meaningful in the sense of measurement theory. When idempotency is assumed, this class reduces to the Boolean max-min ... [more ▼] We give a description of the class of continuous functions that are comparison meaningful in the sense of measurement theory. When idempotency is assumed, this class reduces to the Boolean max-min functions (lattice polynomials). In that case, continuity can be replaced by increasing monotonicity, provided that the domain of definition is open. [less ▲] Detailed reference viewed: 71 (0 UL)An axiomatic approach to the definition of the entropy of a discrete Choquet capacity ; Marichal, Jean-Luc ; in Proc. 9th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2002), Annecy, France, July 1-5, 2002 (2002, July) Detailed reference viewed: 210 (1 UL) |
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