Associative functions :: triangular norms and copulas /
The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process....
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ :
World Scientific,
©2006.
|
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines. This volume offers unique perspectives on aspects of fractals and complexity and, through the examination of complementary techniques, provides a unifying thread in this multidisciplinary endeavour. Do nonlinear interactions play a role in the complexity management of socio-economic-political systems? Is it possible to extract the global properties of genetic regulatory networks without knowing the details of individual genes? What can one learn by transplanting the self-organization effects known in laser processes to the study of emotions? What can the change in the level of complexity tell us about the physiological state of the organism? The reader will enjoy finding the answers to these questions and many more in this book. |
| Beschreibung: | 1 online resource (xiv, 237 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 223-234) and index. |
| ISBN: | 9789812774200 9812774203 1281919349 9781281919342 9812566716 9789812566713 |
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| 520 | |a The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines. This volume offers unique perspectives on aspects of fractals and complexity and, through the examination of complementary techniques, provides a unifying thread in this multidisciplinary endeavour. Do nonlinear interactions play a role in the complexity management of socio-economic-political systems? Is it possible to extract the global properties of genetic regulatory networks without knowing the details of individual genes? What can one learn by transplanting the self-organization effects known in laser processes to the study of emotions? What can the change in the level of complexity tell us about the physiological state of the organism? The reader will enjoy finding the answers to these questions and many more in this book. | ||
| 505 | 0 | |a Preface -- Special symbols -- 1. Introduction. 1.1. Historical notes. 1.2. Preliminaries. 1.3. t-norms and s-norms. 1.4. Copulas -- 2. Representation theorems for associative functions. 2.1. Continuous, Archimedean t-norms. 2.2. Additive and multiplicative generators. 2.3. Extension to arbitrary closed intervals. 2.4. Continuous, non-Archimedean t-norms. 2.5. Non-continuous t-norms. 2.6. Families of t-norms. 2.7. Other representation theorems. 2.8. Related functional equations -- 3. Functional equations involving t-norms. 3.1. Simultaneous associativity. 3.2. n-duality. 3.3. Simple characterizations of Min. 3.4. Homogeneity. 3.5. Distributivity. 3.6. Conical t-norms. 3.7. Rational Archimedean t-norms. 3.8. Extension and sets of uniqueness -- 4. Inequalities involving t-norms. 4.1. Notions of concavity and convexity. 4.2. The dominance relation. 4.3. Uniformly close associative functions. 4.4. Serial iterates and n-copulas. 4.5. Positivity. | |
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| contents | Preface -- Special symbols -- 1. Introduction. 1.1. Historical notes. 1.2. Preliminaries. 1.3. t-norms and s-norms. 1.4. Copulas -- 2. Representation theorems for associative functions. 2.1. Continuous, Archimedean t-norms. 2.2. Additive and multiplicative generators. 2.3. Extension to arbitrary closed intervals. 2.4. Continuous, non-Archimedean t-norms. 2.5. Non-continuous t-norms. 2.6. Families of t-norms. 2.7. Other representation theorems. 2.8. Related functional equations -- 3. Functional equations involving t-norms. 3.1. Simultaneous associativity. 3.2. n-duality. 3.3. Simple characterizations of Min. 3.4. Homogeneity. 3.5. Distributivity. 3.6. Conical t-norms. 3.7. Rational Archimedean t-norms. 3.8. Extension and sets of uniqueness -- 4. Inequalities involving t-norms. 4.1. Notions of concavity and convexity. 4.2. The dominance relation. 4.3. Uniformly close associative functions. 4.4. Serial iterates and n-copulas. 4.5. Positivity. |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Alsina, Claudi. https://id.oclc.org/worldcat/entity/E39PBJjhFYy68wVfrG9tDRHKVC http://id.loc.gov/authorities/names/n79030525 Associative functions : triangular norms and copulas / Claudi Alsina, Maurice J. Frank, Berthold Schweizer. Hackensack, NJ : World Scientific, ©2006. 1 online resource (xiv, 237 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 223-234) and index. Print version record. The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines. This volume offers unique perspectives on aspects of fractals and complexity and, through the examination of complementary techniques, provides a unifying thread in this multidisciplinary endeavour. Do nonlinear interactions play a role in the complexity management of socio-economic-political systems? Is it possible to extract the global properties of genetic regulatory networks without knowing the details of individual genes? What can one learn by transplanting the self-organization effects known in laser processes to the study of emotions? What can the change in the level of complexity tell us about the physiological state of the organism? The reader will enjoy finding the answers to these questions and many more in this book. Preface -- Special symbols -- 1. Introduction. 1.1. Historical notes. 1.2. Preliminaries. 1.3. t-norms and s-norms. 1.4. Copulas -- 2. Representation theorems for associative functions. 2.1. Continuous, Archimedean t-norms. 2.2. Additive and multiplicative generators. 2.3. Extension to arbitrary closed intervals. 2.4. Continuous, non-Archimedean t-norms. 2.5. Non-continuous t-norms. 2.6. Families of t-norms. 2.7. Other representation theorems. 2.8. Related functional equations -- 3. Functional equations involving t-norms. 3.1. Simultaneous associativity. 3.2. n-duality. 3.3. Simple characterizations of Min. 3.4. Homogeneity. 3.5. Distributivity. 3.6. Conical t-norms. 3.7. Rational Archimedean t-norms. 3.8. Extension and sets of uniqueness -- 4. Inequalities involving t-norms. 4.1. Notions of concavity and convexity. 4.2. The dominance relation. 4.3. Uniformly close associative functions. 4.4. Serial iterates and n-copulas. 4.5. Positivity. Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Associative law (Mathematics) http://id.loc.gov/authorities/subjects/sh85008822 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Functional equations Study and teaching Textbooks. Associative law (Mathematics) Study and teaching Textbooks. Mathematical analysis Study and teaching Textbooks. Équations fonctionnelles. Associativité (Mathématiques) Analyse mathématique. MATHEMATICS Functional Analysis. bisacsh Associative law (Mathematics) fast Functional equations fast Mathematical analysis fast Mathematical analysis Study and teaching fast Electronic books. Textbooks fast Schweizer, B. (Berthold) https://id.oclc.org/worldcat/entity/E39PCjGhwWqFBXTxXXmfmfQdHC http://id.loc.gov/authorities/names/n81145090 Frank, Maurice J. https://id.oclc.org/worldcat/entity/E39PCjGRBgKBjdhPqF37YwdbBP http://id.loc.gov/authorities/names/no2006086057 has work: Associative functions (Text) https://id.oclc.org/worldcat/entity/E39PCGphGydqW6ycgChJww47Dy https://id.oclc.org/worldcat/ontology/hasWork Print version: Alsina, Claudi. Associative functions. Hackensack, NJ : World Scientific, ©2006 9812566716 9789812566713 (DLC) 2006284938 (OCoLC)76144355 |
| spellingShingle | Alsina, Claudi Associative functions : triangular norms and copulas / Preface -- Special symbols -- 1. Introduction. 1.1. Historical notes. 1.2. Preliminaries. 1.3. t-norms and s-norms. 1.4. Copulas -- 2. Representation theorems for associative functions. 2.1. Continuous, Archimedean t-norms. 2.2. Additive and multiplicative generators. 2.3. Extension to arbitrary closed intervals. 2.4. Continuous, non-Archimedean t-norms. 2.5. Non-continuous t-norms. 2.6. Families of t-norms. 2.7. Other representation theorems. 2.8. Related functional equations -- 3. Functional equations involving t-norms. 3.1. Simultaneous associativity. 3.2. n-duality. 3.3. Simple characterizations of Min. 3.4. Homogeneity. 3.5. Distributivity. 3.6. Conical t-norms. 3.7. Rational Archimedean t-norms. 3.8. Extension and sets of uniqueness -- 4. Inequalities involving t-norms. 4.1. Notions of concavity and convexity. 4.2. The dominance relation. 4.3. Uniformly close associative functions. 4.4. Serial iterates and n-copulas. 4.5. Positivity. Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Associative law (Mathematics) http://id.loc.gov/authorities/subjects/sh85008822 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Functional equations Study and teaching Textbooks. Associative law (Mathematics) Study and teaching Textbooks. Mathematical analysis Study and teaching Textbooks. Équations fonctionnelles. Associativité (Mathématiques) Analyse mathématique. MATHEMATICS Functional Analysis. bisacsh Associative law (Mathematics) fast Functional equations fast Mathematical analysis fast Mathematical analysis Study and teaching fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052317 http://id.loc.gov/authorities/subjects/sh85008822 http://id.loc.gov/authorities/subjects/sh85082116 |
| title | Associative functions : triangular norms and copulas / |
| title_auth | Associative functions : triangular norms and copulas / |
| title_exact_search | Associative functions : triangular norms and copulas / |
| title_full | Associative functions : triangular norms and copulas / Claudi Alsina, Maurice J. Frank, Berthold Schweizer. |
| title_fullStr | Associative functions : triangular norms and copulas / Claudi Alsina, Maurice J. Frank, Berthold Schweizer. |
| title_full_unstemmed | Associative functions : triangular norms and copulas / Claudi Alsina, Maurice J. Frank, Berthold Schweizer. |
| title_short | Associative functions : |
| title_sort | associative functions triangular norms and copulas |
| title_sub | triangular norms and copulas / |
| topic | Functional equations. http://id.loc.gov/authorities/subjects/sh85052317 Associative law (Mathematics) http://id.loc.gov/authorities/subjects/sh85008822 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Functional equations Study and teaching Textbooks. Associative law (Mathematics) Study and teaching Textbooks. Mathematical analysis Study and teaching Textbooks. Équations fonctionnelles. Associativité (Mathématiques) Analyse mathématique. MATHEMATICS Functional Analysis. bisacsh Associative law (Mathematics) fast Functional equations fast Mathematical analysis fast Mathematical analysis Study and teaching fast |
| topic_facet | Functional equations. Associative law (Mathematics) Mathematical analysis. Functional equations Study and teaching Textbooks. Associative law (Mathematics) Study and teaching Textbooks. Mathematical analysis Study and teaching Textbooks. Équations fonctionnelles. Associativité (Mathématiques) Analyse mathématique. MATHEMATICS Functional Analysis. Functional equations Mathematical analysis Mathematical analysis Study and teaching Electronic books. Textbooks |
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