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On the Poset of Computation Rules for Nonassociative Calculus Couceiro, Miguel ; in Order : A Journal on the Theory of Ordered Sets and its Applications (2012), 30(1), 269-288 Detailed reference viewed: 70 (0 UL)Aggregation functions: Means ; Marichal, Jean-Luc ; et al in Information Sciences (2011), 181(1), 1-22 This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic ... [more ▼] This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic classification on aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with multiple arities (extended means). [less ▲] Detailed reference viewed: 125 (0 UL)Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes ; Marichal, Jean-Luc ; et al in Information Sciences (2011), 181(1), 23-43 In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions ... [more ▼] In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions and on special classes of aggregation functions, covering the well-known conjunctive, disjunctive, and mixed aggregation functions. Some fields of applications are included. [less ▲] Detailed reference viewed: 133 (2 UL)Aggregation functions ; Marichal, Jean-Luc ; et al Book published by Cambridge University Press (2009) Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating ... [more ▼] Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, rigorous and self-contained exposition of aggregation functions. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The properties of each method, as well as their interpretation and analysis, are studied in depth, together with construction methods and practical identification methods. Special attention is given to the nature of scales on which values to be aggregated are defined (ordinal, interval, ratio, bipolar). It is an ideal introduction for graduate students and a unique resource for researchers. [less ▲] Detailed reference viewed: 121 (8 UL)Behavioral analysis of aggregation functions Marichal, Jean-Luc ; ; et al in Bodenhofer, Ulrich; De Baets, Bernard; Klement, Erich Peter (Eds.) et al Proc. 30th Linz Seminar on Fuzzy Set Theory (LINZ 2009): The Legacy of 30 Seminars – Where Do We Stand and Where Do We Go? (2009, February) Detailed reference viewed: 94 (1 UL)Aggregation on bipolar scales ; Marichal, Jean-Luc ; et al in Bodenhofer, Ulrich; De Baets, Bernard; Klement, Erich Peter (Eds.) et al Proc. 30th Linz Seminar on Fuzzy Set Theory (LINZ 2009): The Legacy of 30 Seminars – Where Do We Stand and Where Do We Go? (2009, February) Detailed reference viewed: 93 (0 UL)Infinitary aggregation ; ; et al in Bodenhofer, Ulrich; De Baets, Bernard; Klement, Erich Peter (Eds.) et al Proc. 30th Linz Seminar on Fuzzy Set Theory (LINZ 2009): The Legacy of 30 Seminars – Where Do We Stand and Where Do We Go? (2009, February) In this paper, based on [12, 18], we present infinitary aggregation functions on sequences possessing some a priori given properties. General infinitary aggregation is also discussed, and the connection ... [more ▼] In this paper, based on [12, 18], we present infinitary aggregation functions on sequences possessing some a priori given properties. General infinitary aggregation is also discussed, and the connection with integrals, e.g., Lebesgue, Choquet and Sugeno integrals, is given. [less ▲] Detailed reference viewed: 49 (0 UL)Contribution on some construction methods for aggregation functions ; ; et al In this paper, based on [14], we present some well established construction methods for aggregation functions as well as some new ones. Detailed reference viewed: 40 (0 UL)Monograph: aggregation functions ; Marichal, Jean-Luc ; et al in Acta Polytechnica Hungarica (2009), 6(1), 79-94 There is given a short overview of the monograph "Aggregation Functions" (M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap), Cambridge University Press (in press) with more details from introductory ... [more ▼] There is given a short overview of the monograph "Aggregation Functions" (M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap), Cambridge University Press (in press) with more details from introductory Chapters 1 and 2. [less ▲] Detailed reference viewed: 163 (1 UL)“Aggregation Functions”, Cambridge University Press ; Marichal, Jean-Luc ; et al in Proc. of the 6th Int. Symposium on Intelligent Systems and Informatics (SISY 2008) (2008, September) There is given a short overview of the monograph ”Aggregation Functions” (M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap), Cambridge University Press (in press). Detailed reference viewed: 90 (5 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: 126 (0 UL)Equivalent representations of set functions ; Marichal, Jean-Luc ; in Mathematics of Operations Research (2000), 25(2), 157-178 This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius transformation, and the interactions between elements of any subset of a given set as ... [more ▼] This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation. [less ▲] Detailed reference viewed: 104 (6 UL)Equivalent representations of a set function with applications to game theory and multicriteria decision making ; Marichal, Jean-Luc ; in de Swart, Harrie (Ed.) Proc. of the Int. Conf. on Logic, Game theory and Social choice (LGS'99), Oisterwijk, the Netherlands, May 13-16, 1999 (1999, May) This paper introduces four alternative representations of a set function: the M¨obius transformation, the co-M¨obius transformation, and the interactions between elements of any subset of a given set as ... [more ▼] This paper introduces four alternative representations of a set function: the M¨obius transformation, the co-M¨obius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation. [less ▲] Detailed reference viewed: 46 (0 UL)Equivalent representations of a set function with application to game theory and multicriteria decision making ; Marichal, Jean-Luc ; Scientific Conference (1998, October) Detailed reference viewed: 26 (0 UL) |
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