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 Groupingbased 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 quasicopulas3.5 Disjunctive aggregation functions; 3.6 Uninorms; 3.7 Nullnorms; 3.8 More aggregation functions related to tnorms; 3.9 Restricted distributivity; 4 Means and averages; 4.1 Introduction and definitions; 4.2 Quasiarithmetic means; 4.3 Generalizations of quasiarithmetic 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 aggregationbased 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 Logratio 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 Integralbased 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 integralbased aggregation functions; 11.6 Available software. 
Summary 
A rigorous and selfcontained 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, JeanLuc.


Mesiar, Radko.


Pap, Endre.

Other Form: 
Print version: Grabisch, Michel. Aggregation Functions. Cambridge : Cambridge University Press, ©2009 9780521519267 
ISBN 
9781139641128 

1139641123 

0521519268 

9780521519267 

9781139648738 (electronic bk.) 

113964873X (electronic bk.) 

9781139644150 (electronic bk.) 

1139644157 (electronic bk.) 

9780521519267 
