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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: 102 (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: 114 (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: 112 (8 UL)Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art Marichal, Jean-Luc ; in Aequationes Mathematicae (2009), 77(3), 207-236 We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful ... [more ▼] We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial functions, that is, functions built only on projections and minimum and maximum operations. [less ▲] Detailed reference viewed: 87 (1 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: 42 (0 UL)Contribution on some construction methods for aggregation functions ; ; 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 [14], we present some well established construction methods for aggregation functions as well as some new ones. Detailed reference viewed: 33 (0 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: 74 (1 UL)Aggregation on bipolar scales ; Marichal, Jean-Luc ; et al 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: 149 (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: 64 (1 UL)A complete description of comparison meaningful functions Marichal, Jean-Luc ; ; in Montseny, Eduard; Sobrevilla, Pilar (Eds.) Proceedings of the Joint 4th Conference of the European Society for Fuzzy Logic and Technology and the 11th Rencontres Francophones sur la Logique Floue et ses Applications, Barcelona, Spain, September 7-9, 2005. (2005, September) 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 [less ▲] Detailed reference viewed: 70 (0 UL)A complete description of comparison meaningful functions Marichal, Jean-Luc ; ; in Proc. 3rd Int. Summer School on Aggregation Operators and their Applications (AGOP 2005), Lugano, Switzerland (2005, July) 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: 62 (1 UL)A complete description of comparison meaningful functions Marichal, Jean-Luc ; ; in Aequationes Mathematicae (2005), 69(3), 309-320 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: 63 (4 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: 36 (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 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: 48 (3 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: 59 (0 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: 68 (0 UL) |
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