Aggregation Functions.:
A rigorous and self-contained exposition of aggregation functions and their properties.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2009.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | A rigorous and self-contained exposition of aggregation functions and their properties. |
| Beschreibung: | 1 online resource (480 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139641128 1139641123 0521519268 9780521519267 9781139648738 113964873X 9781139644150 1139644157 |
Internformat
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| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a A rigorous and self-contained exposition of aggregation functions and their properties. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 650 | 0 | |a Numerical functions. |0 http://id.loc.gov/authorities/subjects/sh85093244 | |
| 650 | 0 | |a Aggregation operators. |0 http://id.loc.gov/authorities/subjects/sh2002004486 | |
| 650 | 6 | |a Fonctions numériques. | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn855968924 |
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| adam_text | |
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| author | Grabisch, Michel |
| author2 | Marichal, Jean-Luc Mesiar, Radko Pap, Endre |
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| author_facet | Grabisch, Michel Marichal, Jean-Luc Mesiar, Radko Pap, Endre |
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| callnumber-first | Q - Science |
| callnumber-label | QA246 |
| callnumber-raw | QA246 .A34 2009 |
| callnumber-search | QA246 .A34 2009 |
| callnumber-sort | QA 3246 A34 42009 |
| callnumber-subject | QA - Mathematics |
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| collection | ZDB-4-EBA |
| 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. |
| ctrlnum | (OCoLC)855968924 |
| dewey-full | 511.326 512 |
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| dewey-ones | 511 - General principles of mathematics 512 - Algebra |
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| discipline | Mathematik |
| format | Electronic eBook |
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| genre | Electronic book. Electronic books. |
| genre_facet | Electronic book. Electronic books. |
| id | ZDB-4-EBA-ocn855968924 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:29Z |
| institution | BVB |
| isbn | 9781139641128 1139641123 0521519268 9780521519267 9781139648738 113964873X 9781139644150 1139644157 |
| language | English |
| oclc_num | 855968924 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (480 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications. |
| series2 | Encyclopedia of Mathematics and its Applications |
| spelling | Grabisch, Michel. Aggregation Functions. Cambridge : Cambridge University Press, 2009. 1 online resource (480 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of Mathematics and its Applications Print version record. 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. A rigorous and self-contained exposition of aggregation functions and their properties. Includes bibliographical references and index. Numerical functions. http://id.loc.gov/authorities/subjects/sh85093244 Aggregation operators. http://id.loc.gov/authorities/subjects/sh2002004486 Fonctions numériques. Opérateurs d'agrégation. MATHEMATICS Algebra Intermediate. bisacsh Aggregation operators fast Numerical functions fast Aggregationsoperator gnd http://d-nb.info/gnd/4694009-1 Electronic book. Electronic books. Marichal, Jean-Luc. Mesiar, Radko. Pap, Endre. Print version: Grabisch, Michel. Aggregation Functions. Cambridge : Cambridge University Press, ©2009 9780521519267 Encyclopedia of mathematics and its applications. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=511696 Volltext |
| spellingShingle | Grabisch, Michel Aggregation Functions. Encyclopedia of mathematics and its applications. 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. Numerical functions. http://id.loc.gov/authorities/subjects/sh85093244 Aggregation operators. http://id.loc.gov/authorities/subjects/sh2002004486 Fonctions numériques. Opérateurs d'agrégation. MATHEMATICS Algebra Intermediate. bisacsh Aggregation operators fast Numerical functions fast Aggregationsoperator gnd http://d-nb.info/gnd/4694009-1 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85093244 http://id.loc.gov/authorities/subjects/sh2002004486 http://d-nb.info/gnd/4694009-1 |
| title | Aggregation Functions. |
| title_auth | Aggregation Functions. |
| title_exact_search | Aggregation Functions. |
| title_full | Aggregation Functions. |
| title_fullStr | Aggregation Functions. |
| title_full_unstemmed | Aggregation Functions. |
| title_short | Aggregation Functions. |
| title_sort | aggregation functions |
| topic | Numerical functions. http://id.loc.gov/authorities/subjects/sh85093244 Aggregation operators. http://id.loc.gov/authorities/subjects/sh2002004486 Fonctions numériques. Opérateurs d'agrégation. MATHEMATICS Algebra Intermediate. bisacsh Aggregation operators fast Numerical functions fast Aggregationsoperator gnd http://d-nb.info/gnd/4694009-1 |
| topic_facet | Numerical functions. Aggregation operators. Fonctions numériques. Opérateurs d'agrégation. MATHEMATICS Algebra Intermediate. Aggregation operators Numerical functions Aggregationsoperator Electronic book. Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=511696 |
| work_keys_str_mv | AT grabischmichel aggregationfunctions AT marichaljeanluc aggregationfunctions AT mesiarradko aggregationfunctions AT papendre aggregationfunctions |