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Author Grabisch, Michel.

Title Aggregation Functions.

Imprint Cambridge : Cambridge University Press, 2009.

Item Status

Description 1 online resource (480 pages).
Series Encyclopedia of Mathematics and its Applications
Encyclopedia of mathematics and its applications.
Contents Cover; Half Title; Title Page; Copyright; Dedication; Contents; List of figures; List of tables; Preface; 1. Introduction; 1.1 Main motivations and scope; 1.2 Basic definitions and examples; 1.3 Conventional notation; 2 Properties for aggregation; 2.1 Introduction; 2.2 Elementary mathematical properties; 2.3 Grouping-based properties; 2.4 Invariance properties; 2.5 Further properties; 3 Conjunctive and disjunctive aggregation functions; 3.1 Preliminaries and general notes; 3.2 Generated conjunctive aggregation functions; 3.3 Triangular norms and related conjunctive aggregation functions.
3.4 Copulas and quasi-copulas3.5 Disjunctive aggregation functions; 3.6 Uninorms; 3.7 Nullnorms; 3.8 More aggregation functions related to t-norms; 3.9 Restricted distributivity; 4 Means and averages; 4.1 Introduction and definitions; 4.2 Quasi-arithmetic means; 4.3 Generalizations of quasi-arithmetic means; 4.4 Associative means; 4.5 Means constructed from a mean value property; 4.6 Constructing means; 4.7 Further extended means; 5 Aggregation functions based on nonadditive integrals; 5.1 Introduction; 5.2 Set functions, capacities, and games; 5.3 Some linear transformations of set functions.
5.4 The Choquet integral5.5 The Sugeno integral; 5.6 Other integrals; 6 Construction methods; 6.1 Introduction; 6.2 Transformed aggregation functions; 6.3 Composed aggregation; 6.4 Weighted aggregation functions; 6.5 Some other aggregation-based construction methods; 6.6 Aggregation functions based on minimal dissimilarity; 6.7 Ordinal sums of aggregation functions; 6.8 Extensions to aggregation functions; 7 Aggregation on specific scale types; 7.1 Introduction; 7.2 Ratio scales; 7.3 Difference scales; 7.4 Interval scales; 7.5 Log-ratio scales; 8 Aggregation on ordinal scales.
8.1 Introduction8.2 Order invariant subsets; 8.3 Lattice polynomial functions and some of their properties; 8.4 Ordinal scale invariant functions; 8.5 Comparison meaningful functions on a single ordinal scale; 8.6 Comparison meaningful functions on independent ordinal scales; 8.7 Aggregation on finite chains by chain independent functions; 9 Aggregation on bipolar scales; 9.1 Introduction; 9.2 Associative bipolar operators; 9.3 Minimum and maximum on symmetrized linearly ordered sets; 9.4 Separable aggregation functions; 9.5 Integral-based aggregation functions.
10 Behavioral analysis of aggregation functions10.1 Introduction; 10.2 Expected values and distribution functions; 10.3 Importance indices; 10.4 Interaction indices; 10.5 Maximum improving index; 10.6 Tolerance indices; 10.7 Measures of arguments contribution and involvement; 11 Identification of aggregation functions; 11.1 Introduction; 11.2 General formulation; 11.3 The case of parametrized families of aggregation functions; 11.4 The case of generated aggregation functions; 11.5 The case of integral-based aggregation functions; 11.6 Available software.
Summary A rigorous and self-contained exposition of aggregation functions and their properties.
Bibliography Includes bibliographical references and index.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Numerical functions.
Aggregation operators.
Genre/Form Electronic books.
Electronic book.
Added Author Marichal, Jean-Luc.
Mesiar, Radko.
Pap, Endre.
Other Form: Print version: Grabisch, Michel. Aggregation Functions. Cambridge : Cambridge University Press, ©2009 9780521519267
ISBN 9781139641128
9781139648738 (electronic bk.)
113964873X (electronic bk.)
9781139644150 (electronic bk.)
1139644157 (electronic bk.)