Nonlinear integrals and their applications in data mining:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
©2010
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| Schriftenreihe: | Advances in fuzzy systems
v. 24 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index Ch. 1. Introduction -- ch. 2. Basic knowledge on classical sets. 2.1. Classical sets and set inclusion. 2.2. Set operations. 2.3. Set sequences and set classes. 2.4. Set classes closed under set operations. 2.5. Relations, posets, and lattices. 2.6. The supremum and infimum of real number sets -- ch. 3. Fuzzy sets. 3.1. The membership functions of fuzzy sets. 3.2. Inclusion and operations of fuzzy sets. 3.3. [symbol]-cuts. 3.4. Convex fuzzy sets. 3.5. Decomposition theorems. 3.6. The extension principle. 3.7. Interval numbers. 3.8. Fuzzy numbers and linguistic attribute. 3.9. Binary operations for fuzzy numbers. 3.10. Fuzzy integers -- - ch. 4. Set functions. 4.1. Weights and classical measures. 4.2. Extension of measures. 4.3. Monotone measures. 4.4. [symbol]-measures. 4.5. Quasi-measures. 4.6. Mobius and zeta transformations. 4.7. Belief measures and plausibility measures. 4.8. Necessity measures and possibility measures. 4.9. k-interactive measures. 4.10. Efficiency measures and signed efficiency measures -- ch. 5. Integrations. 5.1. Measurable functions. 5.2. The Riemann integral. 5.3. The Lebesgue-Like integral. 5.4. The Choquet integral. 5.5. Upper and lower integrals. 5.6. r-integrals on finite spaces -- ch. 6. Information fusion. 6.1. Information sources and observations. 6.2. Integrals used as aggregation tools. 6.3. Uncertainty associated with set functions. 6.4. The inverse problem of information fusion -- ch. 7. Optimization and soft computing. 7.1. Basic concepts of optimization. 7.2. Genetic algorithms. 7.3. Pseudo gradient search. 7.4. A hybrid search method -- - ch. 8. Identification of set functions. 8.1. Identification of [symbol]-measures. 8.2. Identification of belief measures. 8.3. Identification of monotone measures. 8.4. Identification of signed efficiency measures by a genetic algorithm. 8.5. Identification of signed efficiency measures by the pseudo gradient. 8.6. Identification of signed efficiency measures based on the Choquet integral by an algebraic method. 8.7. Identification of monotone measures based on r-integrals by a genetic algorithm -- ch. 9. Multiregression based on nonlinear integrals. 9.1. Linear multiregression. 9.2. Nonlinear multiregression based on the Choquet integral. 9.3. A nonlinear multiregression model accommodating both categorical and numerical predictive attributes. 9.4. Advanced consideration on the multiregression involving nonlinear integrals -- - ch. 10. Classifications based on nonlinear integrals. 10.1. Classification by an integral projection. 10.2. Nonlinear classification by weighted Choquet integrals. 10.3. An example of nonlinear classification in a three-dimensional sample space. 10.4. The uniqueness problem of the classification by the Choquet integral with a linear core. 10.5. Advanced consideration on the nonlinear classification involving the Choquet integral -- ch. 11. Data mining with fuzzy data. 11.1. Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI). 11.2. Classification model based on the DCIFI. 11.3. Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI). 11.4. Regression model based on the CIII. Regarding the set of all feature attributes in a given database as the universal set, this monograph discusses various nonadditive set functions that describe the interaction among the contributions from feature attributes towards a considered target attribute. Then, the relevant nonlinear integrals are investigated. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation, nonlinear multiregressions, and nonlinear classifications. Some methods of fuzzification are also introduced for nonlinear integrals such that fuzzy data can be treated and fuzzy information is retrievable. The book is suitable as a text for graduate courses in mathematics, computer science, and information science. It is also useful to researchers in the relevant area |
| Beschreibung: | 1 Online-Ressource (xviii, 340 pages) |
| ISBN: | 9789812814678 9789812814685 9812814671 981281468X |
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| 245 | 1 | 0 | |a Nonlinear integrals and their applications in data mining |c Zhenyuan Wang, Rong Yang, Kwong-Sak Leung |
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Ch. 1. Introduction -- ch. 2. Basic knowledge on classical sets. 2.1. Classical sets and set inclusion. 2.2. Set operations. 2.3. Set sequences and set classes. 2.4. Set classes closed under set operations. 2.5. Relations, posets, and lattices. 2.6. The supremum and infimum of real number sets -- ch. 3. Fuzzy sets. 3.1. The membership functions of fuzzy sets. 3.2. Inclusion and operations of fuzzy sets. 3.3. [symbol]-cuts. 3.4. Convex fuzzy sets. 3.5. Decomposition theorems. 3.6. The extension principle. 3.7. Interval numbers. 3.8. Fuzzy numbers and linguistic attribute. 3.9. Binary operations for fuzzy numbers. 3.10. Fuzzy integers -- | ||
| 500 | |a - ch. 4. Set functions. 4.1. Weights and classical measures. 4.2. Extension of measures. 4.3. Monotone measures. 4.4. [symbol]-measures. 4.5. Quasi-measures. 4.6. Mobius and zeta transformations. 4.7. Belief measures and plausibility measures. 4.8. Necessity measures and possibility measures. 4.9. k-interactive measures. 4.10. Efficiency measures and signed efficiency measures -- ch. 5. Integrations. 5.1. Measurable functions. 5.2. The Riemann integral. 5.3. The Lebesgue-Like integral. 5.4. The Choquet integral. 5.5. Upper and lower integrals. 5.6. r-integrals on finite spaces -- ch. 6. Information fusion. 6.1. Information sources and observations. 6.2. Integrals used as aggregation tools. 6.3. Uncertainty associated with set functions. 6.4. The inverse problem of information fusion -- ch. 7. Optimization and soft computing. 7.1. Basic concepts of optimization. 7.2. Genetic algorithms. 7.3. Pseudo gradient search. 7.4. A hybrid search method -- | ||
| 500 | |a - ch. 8. Identification of set functions. 8.1. Identification of [symbol]-measures. 8.2. Identification of belief measures. 8.3. Identification of monotone measures. 8.4. Identification of signed efficiency measures by a genetic algorithm. 8.5. Identification of signed efficiency measures by the pseudo gradient. 8.6. Identification of signed efficiency measures based on the Choquet integral by an algebraic method. 8.7. Identification of monotone measures based on r-integrals by a genetic algorithm -- ch. 9. Multiregression based on nonlinear integrals. 9.1. Linear multiregression. 9.2. Nonlinear multiregression based on the Choquet integral. 9.3. A nonlinear multiregression model accommodating both categorical and numerical predictive attributes. 9.4. Advanced consideration on the multiregression involving nonlinear integrals -- | ||
| 500 | |a - ch. 10. Classifications based on nonlinear integrals. 10.1. Classification by an integral projection. 10.2. Nonlinear classification by weighted Choquet integrals. 10.3. An example of nonlinear classification in a three-dimensional sample space. 10.4. The uniqueness problem of the classification by the Choquet integral with a linear core. 10.5. Advanced consideration on the nonlinear classification involving the Choquet integral -- ch. 11. Data mining with fuzzy data. 11.1. Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI). 11.2. Classification model based on the DCIFI. 11.3. Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI). 11.4. Regression model based on the CIII. | ||
| 500 | |a Regarding the set of all feature attributes in a given database as the universal set, this monograph discusses various nonadditive set functions that describe the interaction among the contributions from feature attributes towards a considered target attribute. Then, the relevant nonlinear integrals are investigated. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation, nonlinear multiregressions, and nonlinear classifications. Some methods of fuzzification are also introduced for nonlinear integrals such that fuzzy data can be treated and fuzzy information is retrievable. The book is suitable as a text for graduate courses in mathematics, computer science, and information science. It is also useful to researchers in the relevant area | ||
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| 650 | 4 | |a Fuzzy sets | |
| 650 | 4 | |a Integrals | |
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Datensatz im Suchindex
| _version_ | 1804175572314619904 |
|---|---|
| any_adam_object | |
| author | Wang, Zhenyuan |
| author_facet | Wang, Zhenyuan |
| author_role | aut |
| author_sort | Wang, Zhenyuan |
| author_variant | z w zw |
| building | Verbundindex |
| bvnumber | BV043132020 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)738438068 (DE-599)BVBBV043132020 |
| dewey-full | 511.313 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.313 |
| dewey-search | 511.313 |
| dewey-sort | 3511.313 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043132020 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:25Z |
| institution | BVB |
| isbn | 9789812814678 9789812814685 9812814671 981281468X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028556210 |
| oclc_num | 738438068 |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xviii, 340 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| series2 | Advances in fuzzy systems |
| spelling | Wang, Zhenyuan Verfasser aut Nonlinear integrals and their applications in data mining Zhenyuan Wang, Rong Yang, Kwong-Sak Leung Singapore World Scientific ©2010 1 Online-Ressource (xviii, 340 pages) txt rdacontent c rdamedia cr rdacarrier Advances in fuzzy systems v. 24 Includes bibliographical references and index Ch. 1. Introduction -- ch. 2. Basic knowledge on classical sets. 2.1. Classical sets and set inclusion. 2.2. Set operations. 2.3. Set sequences and set classes. 2.4. Set classes closed under set operations. 2.5. Relations, posets, and lattices. 2.6. The supremum and infimum of real number sets -- ch. 3. Fuzzy sets. 3.1. The membership functions of fuzzy sets. 3.2. Inclusion and operations of fuzzy sets. 3.3. [symbol]-cuts. 3.4. Convex fuzzy sets. 3.5. Decomposition theorems. 3.6. The extension principle. 3.7. Interval numbers. 3.8. Fuzzy numbers and linguistic attribute. 3.9. Binary operations for fuzzy numbers. 3.10. Fuzzy integers -- - ch. 4. Set functions. 4.1. Weights and classical measures. 4.2. Extension of measures. 4.3. Monotone measures. 4.4. [symbol]-measures. 4.5. Quasi-measures. 4.6. Mobius and zeta transformations. 4.7. Belief measures and plausibility measures. 4.8. Necessity measures and possibility measures. 4.9. k-interactive measures. 4.10. Efficiency measures and signed efficiency measures -- ch. 5. Integrations. 5.1. Measurable functions. 5.2. The Riemann integral. 5.3. The Lebesgue-Like integral. 5.4. The Choquet integral. 5.5. Upper and lower integrals. 5.6. r-integrals on finite spaces -- ch. 6. Information fusion. 6.1. Information sources and observations. 6.2. Integrals used as aggregation tools. 6.3. Uncertainty associated with set functions. 6.4. The inverse problem of information fusion -- ch. 7. Optimization and soft computing. 7.1. Basic concepts of optimization. 7.2. Genetic algorithms. 7.3. Pseudo gradient search. 7.4. A hybrid search method -- - ch. 8. Identification of set functions. 8.1. Identification of [symbol]-measures. 8.2. Identification of belief measures. 8.3. Identification of monotone measures. 8.4. Identification of signed efficiency measures by a genetic algorithm. 8.5. Identification of signed efficiency measures by the pseudo gradient. 8.6. Identification of signed efficiency measures based on the Choquet integral by an algebraic method. 8.7. Identification of monotone measures based on r-integrals by a genetic algorithm -- ch. 9. Multiregression based on nonlinear integrals. 9.1. Linear multiregression. 9.2. Nonlinear multiregression based on the Choquet integral. 9.3. A nonlinear multiregression model accommodating both categorical and numerical predictive attributes. 9.4. Advanced consideration on the multiregression involving nonlinear integrals -- - ch. 10. Classifications based on nonlinear integrals. 10.1. Classification by an integral projection. 10.2. Nonlinear classification by weighted Choquet integrals. 10.3. An example of nonlinear classification in a three-dimensional sample space. 10.4. The uniqueness problem of the classification by the Choquet integral with a linear core. 10.5. Advanced consideration on the nonlinear classification involving the Choquet integral -- ch. 11. Data mining with fuzzy data. 11.1. Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI). 11.2. Classification model based on the DCIFI. 11.3. Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI). 11.4. Regression model based on the CIII. Regarding the set of all feature attributes in a given database as the universal set, this monograph discusses various nonadditive set functions that describe the interaction among the contributions from feature attributes towards a considered target attribute. Then, the relevant nonlinear integrals are investigated. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation, nonlinear multiregressions, and nonlinear classifications. Some methods of fuzzification are also introduced for nonlinear integrals such that fuzzy data can be treated and fuzzy information is retrievable. The book is suitable as a text for graduate courses in mathematics, computer science, and information science. It is also useful to researchers in the relevant area Mathematics Computer science MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Informatik Mathematik Fuzzy sets Integrals Fuzzy logic Data mining Data Mining (DE-588)4428654-5 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf Nichtlineare Integralgleichung (DE-588)4240925-1 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 s Nichtlineare Integralgleichung (DE-588)4240925-1 s Data Mining (DE-588)4428654-5 s 1\p DE-604 Yang, Rong Sonstige oth Leung, Kwong Sak Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=374861 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wang, Zhenyuan Nonlinear integrals and their applications in data mining Mathematics Computer science MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Informatik Mathematik Fuzzy sets Integrals Fuzzy logic Data mining Data Mining (DE-588)4428654-5 gnd Fuzzy-Logik (DE-588)4341284-1 gnd Nichtlineare Integralgleichung (DE-588)4240925-1 gnd |
| subject_GND | (DE-588)4428654-5 (DE-588)4341284-1 (DE-588)4240925-1 |
| title | Nonlinear integrals and their applications in data mining |
| title_auth | Nonlinear integrals and their applications in data mining |
| title_exact_search | Nonlinear integrals and their applications in data mining |
| title_full | Nonlinear integrals and their applications in data mining Zhenyuan Wang, Rong Yang, Kwong-Sak Leung |
| title_fullStr | Nonlinear integrals and their applications in data mining Zhenyuan Wang, Rong Yang, Kwong-Sak Leung |
| title_full_unstemmed | Nonlinear integrals and their applications in data mining Zhenyuan Wang, Rong Yang, Kwong-Sak Leung |
| title_short | Nonlinear integrals and their applications in data mining |
| title_sort | nonlinear integrals and their applications in data mining |
| topic | Mathematics Computer science MATHEMATICS / Infinity bisacsh MATHEMATICS / Logic bisacsh Informatik Mathematik Fuzzy sets Integrals Fuzzy logic Data mining Data Mining (DE-588)4428654-5 gnd Fuzzy-Logik (DE-588)4341284-1 gnd Nichtlineare Integralgleichung (DE-588)4240925-1 gnd |
| topic_facet | Mathematics Computer science MATHEMATICS / Infinity MATHEMATICS / Logic Informatik Mathematik Fuzzy sets Integrals Fuzzy logic Data mining Data Mining Fuzzy-Logik Nichtlineare Integralgleichung |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=374861 |
| work_keys_str_mv | AT wangzhenyuan nonlinearintegralsandtheirapplicationsindatamining AT yangrong nonlinearintegralsandtheirapplicationsindatamining AT leungkwongsak nonlinearintegralsandtheirapplicationsindatamining |