Aggregation functions: a guide for practitioners
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Series: | Studies in fuzziness and soft computing
221 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 361 S. |
| ISBN: | 9783540737209 3540737200 |
Staff View
MARC
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| 100 | 1 | |a Beliakov, Gleb |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Aggregation functions |b a guide for practitioners |c Gleb Beliakov ; Ana Pradera ; Tomasa Calvo |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XIX, 361 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Studies in fuzziness and soft computing |v 221 | |
| 650 | 4 | |a Aggregation operators | |
| 650 | 4 | |a Multiple criteria decision making | |
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| 700 | 1 | |a Calvo, Tomasa |d 1954- |e Verfasser |0 (DE-588)123554373 |4 aut | |
| 830 | 0 | |a Studies in fuzziness and soft computing |v 221 |w (DE-604)BV021858135 |9 221 | |
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Record in the Search Index
| _version_ | 1804138462408867840 |
|---|---|
| adam_text | Contents
Introduction
............................................... 1
1.1
What is an aggregation function?
.......................... 1
1.2
What are aggregation functions used for?
................... 5
1.3
Classification and general properties
....................... 8
1.3.1
Main classes
...................................... 8
1.3.2
Main properties
................................... 9
1.3.3
Duality
.......................................... 18
1.3.4
Comparability
.................................... 20
1.3.5
Continuity and stability
............................ 21
1.4
Main families and prototypical examples
................... 23
1.4.1
Min
and Max
..................................... 23
1.4.2
Means
........................................... 24
1.4.3
Medians
.......................................... 25
1.4.4
Ordered weighted averaging
........................ 25
1.4.5
Choquet and Sugeno integrals
....................... 26
1.4.6
Conjunctive and disjunctive functions
................ 27
1.4.7
Mixed aggregation
................................. 28
1.5
Composition and transformation of aggregation functions
..... 28
1.6
How to choose an aggregation function
..................... 31
1.7
Numerical approximation and optimization tools
............ 34
1.8
Key references
.......................................... 37
Averaging Functions
....................................... 39
2.1
Semantics
.............................................. 39
2.2
Classical means
......................................... 40
2.3
Weighted quasi-arithmetic means
.......................... 48
2.3.1
Definitions
....................................... 48
2.3.2
Main properties
................................... 48
2.3.3
Examples
........................................ 49
2.3.4
Calculation
....................................... 53
2.3.5
Weighting triangles
................................ 54
XVI Contents
2.3.6
Weights dispersion
................................. 56
2.3.7
How to choose weights
............................. 57
2.4
Other means
............................................ 62
2.4.1
Gini
means
....................................... 62
2.4.2
Bonferroni means
.................................. 63
2.4.3
Heronian mean
.................................... 64
2.4.4
Generalized logarithmic means
...................... 65
2.4.5
Mean of Bajraktarevic
............................. 66
2.5
Ordered Weighted Averaging
.............................. 68
2.5.1
Definitions
....................................... 68
2.5.2
Main properties
................................... 69
2.5.3
Other types of
OWA
functions
...................... 71
2.5.4
Generalized
OWA
................................. 73
2.5.5
How to choose weights in
OWA
..................... 77
2.5.6
Choosing parameters of generalized
OWA
............ 87
2.6
Choquet Integral
........................................ 90
2.6.1
Semantics
........................................ 90
2.6.2
Definitions and properties
.......................... 92
2.6.3
Types of fuzzy measures
............................ 98
2.6.4
Interaction, importance and other indices
.............105
2.6.5
Special cases of the Choquet integral
.................109
2.6.6
Fitting fuzzy measures
.............................110
2.6.7
Generalized Choquet integral
.......................115
2.7
Sugeno Integral
.........................................116
2.7.1
Definition and properties
...........................116
2.8
Medians and order statistics
..............................119
2.8.1
Median
..........................................119
2.8.2
Order statistics
...................................122
2.9
Key references
..........................................122
3
Conjunctive and Disjunctive Functions
....................123
3.1
Semantics
..............................................123
3.2
Duality
................................................124
3.3
Generalized OR and AND
-
functions
......................124
3.4
Triangular norms and conorms
............................126
3.4.1
Definitions
.......................................126
3.4.2
Main properties
...................................129
3.4.3
Strict and
nilpotent t-norms
and t-conorms
..........132
3.4.4
Archimedean t-norms and t-conorms
................134
3.4.5
Additive and multiplicative generators
...............135
3.4.6
Pseudo-inverses
...................................138
3.4.7
Isomorphic t-norms
...............................140
3.4.8
Comparison of continuous Archimedean t-norms
......143
3.4.9
Ordinal sums
.....................................144
3.4.10
Approximation of continuous t-norms
................148
Contents XVII
3.4.11
Families
of
t-norms
................................149
3.4.12
Lipschitz-continuity
...............................167
3.4.13
Calculation.......................................
169
3.4.14
How to choose a triangular norm/conorm
............170
3.4.15
How to fit additive generators
.......................172
3.4.16
Introduction of weights
.............................176
3.5
Copulas and dual copulas
.................................182
3.6
Other conjunctive and disjunctive functions
.................186
3.7
Noble reinforcement
.....................................190
3.8
Key references
..........................................196
Mixed Functions
...........................................197
4.1
Semantics
..............................................197
4.2
Uninorms
..............................................200
4.2.1
Definition
........................................200
4.2.2
Main properties
...................................200
4.2.3
Main classes of uninorms
...........................202
4.2.4
Examples
........................................206
4.2.5
Calculation
.......................................211
4.2.6
Fitting to the data
................................211
4.3
Nullnorms
..............................................214
4.3.1
Definition
........................................214
4.3.2
Main properties
...................................215
4.3.3
Examples
........................................217
4.3.4
Calculation
.......................................218
4.3.5
Fitting to the data
................................219
4.4
Generated functions
.....................................220
4.4.1
Definitions
.......................................221
4.4.2
Main properties
...................................223
4.4.3
Classes of generated functions
.......................224
4.4.4
Examples
........................................227
4.4.5
Fitting to the data
................................230
4.5
Т
-S
functions
...........................................230
4.5.1
Definitions
.......................................231
4.5.2
Main properties
...................................233
4.5.3
Examples
........................................234
4.5.4
Fitting to the data
................................236
4.6
Symmetric sums
.........................................239
4.6.1
Definitions
.......................................240
4.6.2
Main properties
...................................241
4.6.3
Examples
........................................244
4.6.4
Fitting to the data
................................249
4.7
ST-OWA functions
......................................249
4.7.1
Definitions
.......................................249
4.7.2
Main properties
...................................251
XVIII
Contents
4.7.3
Examples
........................................254
4.7.4
U-OWA functions
.................................256
4.7.5
Fitting to the data
................................257
4.8
Key references
..........................................260
5
Choice and Construction of Aggregation Functions
........261
5.1
Problem formalization
...................................261
5.2
Fitting empirical data
....................................262
5.3
General problem formulation
..............................263
5.4
Special cases
............................................264
5.4.1
Linearization of outputs
............................268
5.5
Assessment of suitability
.................................269
6
Interpolatory
Type Aggregation Functions
.................271
6.1
Semantics
..............................................271
6.2
Construction based on spline functions
.....................272
6.2.1
Problem formulation
...............................272
6.2.2
Preservation of specific properties
...................273
6.3
Construction based on Lipschitz interpolation
...............276
6.4
Preservation of specific properties
.........................278
6.4.1
Conjunctive, disjunctive and averaging behavior
.......278
6.4.2
Absorbing element
.................................279
6.4.3
Neutral element
...................................279
6.4.4
Mixed behavior
...................................281
6.4.5
Given diagonal and opposite diagonal
................284
6.4.6
Given marginals
...................................286
6.4.7
Noble reinforcement
...............................290
7
Other Types of Aggregation and Additional Properties
.... 297
7.1
Other types of aggregation
................................297
7.2
Some additional properties
...............................301
A Tools for Approximation and Optimization
................305
A.
1
Univariate interpolation
..................................305
A.2 Univariate approximation and smoothing
...................307
A.3 Approximation with constraints
...........................309
A.4 Multivariate approximation
...............................312
A.5 Convex and non-convex optimization
.......................316
A.5.1 Univariate optimization
............................318
A.5.2 Multivariate constrained optimization
................319
A.5.3 Multilevel optimization
.............................322
A.5.4 Global optimization: stochastic methods
..............323
A.5.5 Global optimization: deterministic methods
...........324
A.6 Main tools and libraries
..................................324
Contents XIX
В
Problems..................................................329
References
.....................................................341
Index
..........................................................355
|
| any_adam_object | 1 |
| author | Beliakov, Gleb Pradera, Ana Calvo, Tomasa 1954- |
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| discipline | Informatik Mathematik |
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| id | DE-604.BV035206496 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:28:34Z |
| institution | BVB |
| isbn | 9783540737209 3540737200 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017012825 |
| oclc_num | 166372534 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XIX, 361 S. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Studies in fuzziness and soft computing |
| series2 | Studies in fuzziness and soft computing |
| spelling | Beliakov, Gleb Verfasser aut Aggregation functions a guide for practitioners Gleb Beliakov ; Ana Pradera ; Tomasa Calvo Berlin [u.a.] Springer 2007 XIX, 361 S. txt rdacontent n rdamedia nc rdacarrier Studies in fuzziness and soft computing 221 Aggregation operators Multiple criteria decision making Software engineering Aggregationsoperator (DE-588)4694009-1 gnd rswk-swf Aggregationsoperator (DE-588)4694009-1 s DE-604 Pradera, Ana Verfasser aut Calvo, Tomasa 1954- Verfasser (DE-588)123554373 aut Studies in fuzziness and soft computing 221 (DE-604)BV021858135 221 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017012825&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beliakov, Gleb Pradera, Ana Calvo, Tomasa 1954- Aggregation functions a guide for practitioners Studies in fuzziness and soft computing Aggregation operators Multiple criteria decision making Software engineering Aggregationsoperator (DE-588)4694009-1 gnd |
| subject_GND | (DE-588)4694009-1 |
| title | Aggregation functions a guide for practitioners |
| title_auth | Aggregation functions a guide for practitioners |
| title_exact_search | Aggregation functions a guide for practitioners |
| title_full | Aggregation functions a guide for practitioners Gleb Beliakov ; Ana Pradera ; Tomasa Calvo |
| title_fullStr | Aggregation functions a guide for practitioners Gleb Beliakov ; Ana Pradera ; Tomasa Calvo |
| title_full_unstemmed | Aggregation functions a guide for practitioners Gleb Beliakov ; Ana Pradera ; Tomasa Calvo |
| title_short | Aggregation functions |
| title_sort | aggregation functions a guide for practitioners |
| title_sub | a guide for practitioners |
| topic | Aggregation operators Multiple criteria decision making Software engineering Aggregationsoperator (DE-588)4694009-1 gnd |
| topic_facet | Aggregation operators Multiple criteria decision making Software engineering Aggregationsoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017012825&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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