Nonlinear integrals and their applications in data mining /:
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...
Gespeichert in:
1. Verfasser: | |
---|---|
Weitere Verfasser: | , |
Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2010.
|
Schriftenreihe: | Advances in fuzzy systems ;
v. 24. |
Schlagworte: | |
Online-Zugang: | Volltext |
Zusammenfassung: | 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 resource (xviii, 340 pages) : illustrations |
Bibliographie: | Includes bibliographical references and index. |
ISBN: | 9789812814685 981281468X |
Internformat
MARC
LEADER | 00000cam a2200000 a 4500 | ||
---|---|---|---|
001 | ZDB-4-EBA-ocn738438068 | ||
003 | OCoLC | ||
005 | 20241004212047.0 | ||
006 | m o d | ||
007 | cr cnu---unuuu | ||
008 | 110705s2010 si a ob 001 0 eng d | ||
040 | |a N$T |b eng |e pn |c N$T |d EBLCP |d E7B |d I9W |d OCLCQ |d DEBSZ |d YDXCP |d OCLCQ |d OCLCF |d OCLCQ |d AZK |d LOA |d JBG |d AGLDB |d MOR |d PIFAG |d ZCU |d MERUC |d OCLCQ |d U3W |d STF |d WRM |d OCLCQ |d VTS |d NRAMU |d ICG |d INT |d VT2 |d AU@ |d OCLCQ |d WYU |d OCLCQ |d DKC |d OCLCQ |d M8D |d UKAHL |d OCLCQ |d LEAUB |d UKCRE |d AJS |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d OCLCL |d SXB |d OCLCQ | ||
015 | |a GBA937228 |2 bnb | ||
016 | 7 | |a 015109980 |2 Uk | |
019 | |a 961519311 |a 962639794 |a 968290138 |a 988407968 |a 992077218 |a 1037795718 |a 1038666219 |a 1045440218 |a 1055383111 |a 1058110585 |a 1058501774 |a 1066414716 |a 1081291304 |a 1086434668 |a 1153496663 | ||
020 | |a 9789812814685 |q (electronic bk.) | ||
020 | |a 981281468X |q (electronic bk.) | ||
020 | |z 9812814671 | ||
020 | |z 9789812814678 | ||
035 | |a (OCoLC)738438068 |z (OCoLC)961519311 |z (OCoLC)962639794 |z (OCoLC)968290138 |z (OCoLC)988407968 |z (OCoLC)992077218 |z (OCoLC)1037795718 |z (OCoLC)1038666219 |z (OCoLC)1045440218 |z (OCoLC)1055383111 |z (OCoLC)1058110585 |z (OCoLC)1058501774 |z (OCoLC)1066414716 |z (OCoLC)1081291304 |z (OCoLC)1086434668 |z (OCoLC)1153496663 | ||
050 | 4 | |a QA248.5 |b .W36 2010eb | |
072 | 7 | |a MAT |x 016000 |2 bisacsh | |
072 | 7 | |a MAT |x 018000 |2 bisacsh | |
082 | 7 | |a 511.313 |2 22 | |
049 | |a MAIN | ||
100 | 1 | |a Wang, Zhenyuan. | |
245 | 1 | 0 | |a Nonlinear integrals and their applications in data mining / |c Zhenyuan Wang, Rong Yang, Kwong-Sak Leung. |
260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2010. | ||
300 | |a 1 online resource (xviii, 340 pages) : |b illustrations | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
490 | 1 | |a Advances in fuzzy systems ; |v v. 17 [i.e. 24] | |
504 | |a Includes bibliographical references and index. | ||
505 | 0 | |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 -- 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. | |
520 | |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. | ||
588 | 0 | |a Print version record. | |
650 | 0 | |a Fuzzy sets. |0 http://id.loc.gov/authorities/subjects/sh85052627 | |
650 | 0 | |a Integrals. |0 http://id.loc.gov/authorities/subjects/sh85067099 | |
650 | 0 | |a Fuzzy logic. |0 http://id.loc.gov/authorities/subjects/sh93006704 | |
650 | 0 | |a Data mining. |0 http://id.loc.gov/authorities/subjects/sh97002073 | |
650 | 6 | |a Ensembles flous. | |
650 | 6 | |a Intégrales. | |
650 | 6 | |a Logique floue. | |
650 | 6 | |a Exploration de données (Informatique) | |
650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
650 | 7 | |a Data mining |2 fast | |
650 | 7 | |a Fuzzy logic |2 fast | |
650 | 7 | |a Fuzzy sets |2 fast | |
650 | 7 | |a Integrals |2 fast | |
700 | 1 | |a Yang, Rong. | |
700 | 1 | |a Leung, Kwong Sak, |d 1955- |1 https://id.oclc.org/worldcat/entity/E39PCjyBw8bGfktDVytHCXtMyd |0 http://id.loc.gov/authorities/names/n99837297 | |
776 | 0 | 8 | |i Print version: |a Wang, Zhenyuan. |t Nonlinear integrals and their applications in data mining. |d Singapore ; Hackensack, NJ : World Scientific, ©2010 |z 9812814671 |w (OCoLC)228425518 |
830 | 0 | |a Advances in fuzzy systems ; |v v. 24. |0 http://id.loc.gov/authorities/names/n94081927 | |
856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374861 |3 Volltext |
938 | |a Askews and Holts Library Services |b ASKH |n AH24685786 | ||
938 | |a EBL - Ebook Library |b EBLB |n EBL731074 | ||
938 | |a ebrary |b EBRY |n ebr10480244 | ||
938 | |a EBSCOhost |b EBSC |n 374861 | ||
938 | |a YBP Library Services |b YANK |n 6965022 | ||
994 | |a 92 |b GEBAY | ||
912 | |a ZDB-4-EBA | ||
049 | |a DE-863 |
Datensatz im Suchindex
DE-BY-FWS_katkey | ZDB-4-EBA-ocn738438068 |
---|---|
_version_ | 1816881763786424320 |
adam_text | |
any_adam_object | |
author | Wang, Zhenyuan |
author2 | Yang, Rong Leung, Kwong Sak, 1955- |
author2_role | |
author2_variant | r y ry k s l ks ksl |
author_GND | http://id.loc.gov/authorities/names/n99837297 |
author_facet | Wang, Zhenyuan Yang, Rong Leung, Kwong Sak, 1955- |
author_role | |
author_sort | Wang, Zhenyuan |
author_variant | z w zw |
building | Verbundindex |
bvnumber | localFWS |
callnumber-first | Q - Science |
callnumber-label | QA248 |
callnumber-raw | QA248.5 .W36 2010eb |
callnumber-search | QA248.5 .W36 2010eb |
callnumber-sort | QA 3248.5 W36 42010EB |
callnumber-subject | QA - Mathematics |
collection | ZDB-4-EBA |
contents | 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. |
ctrlnum | (OCoLC)738438068 |
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 |
fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>07514cam a2200709 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn738438068</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">110705s2010 si a ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">EBLCP</subfield><subfield code="d">E7B</subfield><subfield code="d">I9W</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AZK</subfield><subfield code="d">LOA</subfield><subfield code="d">JBG</subfield><subfield code="d">AGLDB</subfield><subfield code="d">MOR</subfield><subfield code="d">PIFAG</subfield><subfield code="d">ZCU</subfield><subfield code="d">MERUC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">U3W</subfield><subfield code="d">STF</subfield><subfield code="d">WRM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">NRAMU</subfield><subfield code="d">ICG</subfield><subfield code="d">INT</subfield><subfield code="d">VT2</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">M8D</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">LEAUB</subfield><subfield code="d">UKCRE</subfield><subfield code="d">AJS</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">SXB</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">GBA937228</subfield><subfield code="2">bnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">015109980</subfield><subfield code="2">Uk</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">961519311</subfield><subfield code="a">962639794</subfield><subfield code="a">968290138</subfield><subfield code="a">988407968</subfield><subfield code="a">992077218</subfield><subfield code="a">1037795718</subfield><subfield code="a">1038666219</subfield><subfield code="a">1045440218</subfield><subfield code="a">1055383111</subfield><subfield code="a">1058110585</subfield><subfield code="a">1058501774</subfield><subfield code="a">1066414716</subfield><subfield code="a">1081291304</subfield><subfield code="a">1086434668</subfield><subfield code="a">1153496663</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812814685</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">981281468X</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9812814671</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9789812814678</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)738438068</subfield><subfield code="z">(OCoLC)961519311</subfield><subfield code="z">(OCoLC)962639794</subfield><subfield code="z">(OCoLC)968290138</subfield><subfield code="z">(OCoLC)988407968</subfield><subfield code="z">(OCoLC)992077218</subfield><subfield code="z">(OCoLC)1037795718</subfield><subfield code="z">(OCoLC)1038666219</subfield><subfield code="z">(OCoLC)1045440218</subfield><subfield code="z">(OCoLC)1055383111</subfield><subfield code="z">(OCoLC)1058110585</subfield><subfield code="z">(OCoLC)1058501774</subfield><subfield code="z">(OCoLC)1066414716</subfield><subfield code="z">(OCoLC)1081291304</subfield><subfield code="z">(OCoLC)1086434668</subfield><subfield code="z">(OCoLC)1153496663</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA248.5</subfield><subfield code="b">.W36 2010eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">016000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">018000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">511.313</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wang, Zhenyuan.</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear integrals and their applications in data mining /</subfield><subfield code="c">Zhenyuan Wang, Rong Yang, Kwong-Sak Leung.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">Hackensack, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2010.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xviii, 340 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Advances in fuzzy systems ;</subfield><subfield code="v">v. 17 [i.e. 24]</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="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 -- 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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Fuzzy sets.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85052627</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Integrals.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85067099</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Fuzzy logic.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh93006704</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Data mining.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh97002073</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Ensembles flous.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Intégrales.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Logique floue.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Exploration de données (Informatique)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Infinity.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Logic.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Data mining</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fuzzy logic</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fuzzy sets</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Integrals</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yang, Rong.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Leung, Kwong Sak,</subfield><subfield code="d">1955-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjyBw8bGfktDVytHCXtMyd</subfield><subfield code="0">http://id.loc.gov/authorities/names/n99837297</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Wang, Zhenyuan.</subfield><subfield code="t">Nonlinear integrals and their applications in data mining.</subfield><subfield code="d">Singapore ; Hackensack, NJ : World Scientific, ©2010</subfield><subfield code="z">9812814671</subfield><subfield code="w">(OCoLC)228425518</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Advances in fuzzy systems ;</subfield><subfield code="v">v. 24.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n94081927</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374861</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24685786</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL731074</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10480244</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">374861</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">6965022</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
id | ZDB-4-EBA-ocn738438068 |
illustrated | Illustrated |
indexdate | 2024-11-27T13:17:53Z |
institution | BVB |
isbn | 9789812814685 981281468X |
language | English |
oclc_num | 738438068 |
open_access_boolean | |
owner | MAIN DE-863 DE-BY-FWS |
owner_facet | MAIN DE-863 DE-BY-FWS |
physical | 1 online resource (xviii, 340 pages) : illustrations |
psigel | ZDB-4-EBA |
publishDate | 2010 |
publishDateSearch | 2010 |
publishDateSort | 2010 |
publisher | World Scientific, |
record_format | marc |
series | Advances in fuzzy systems ; |
series2 | Advances in fuzzy systems ; |
spelling | Wang, Zhenyuan. Nonlinear integrals and their applications in data mining / Zhenyuan Wang, Rong Yang, Kwong-Sak Leung. Singapore ; Hackensack, NJ : World Scientific, ©2010. 1 online resource (xviii, 340 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Advances in fuzzy systems ; v. 17 [i.e. 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. Print version record. Fuzzy sets. http://id.loc.gov/authorities/subjects/sh85052627 Integrals. http://id.loc.gov/authorities/subjects/sh85067099 Fuzzy logic. http://id.loc.gov/authorities/subjects/sh93006704 Data mining. http://id.loc.gov/authorities/subjects/sh97002073 Ensembles flous. Intégrales. Logique floue. Exploration de données (Informatique) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Data mining fast Fuzzy logic fast Fuzzy sets fast Integrals fast Yang, Rong. Leung, Kwong Sak, 1955- https://id.oclc.org/worldcat/entity/E39PCjyBw8bGfktDVytHCXtMyd http://id.loc.gov/authorities/names/n99837297 Print version: Wang, Zhenyuan. Nonlinear integrals and their applications in data mining. Singapore ; Hackensack, NJ : World Scientific, ©2010 9812814671 (OCoLC)228425518 Advances in fuzzy systems ; v. 24. http://id.loc.gov/authorities/names/n94081927 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374861 Volltext |
spellingShingle | Wang, Zhenyuan Nonlinear integrals and their applications in data mining / Advances in fuzzy systems ; 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. Fuzzy sets. http://id.loc.gov/authorities/subjects/sh85052627 Integrals. http://id.loc.gov/authorities/subjects/sh85067099 Fuzzy logic. http://id.loc.gov/authorities/subjects/sh93006704 Data mining. http://id.loc.gov/authorities/subjects/sh97002073 Ensembles flous. Intégrales. Logique floue. Exploration de données (Informatique) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Data mining fast Fuzzy logic fast Fuzzy sets fast Integrals fast |
subject_GND | http://id.loc.gov/authorities/subjects/sh85052627 http://id.loc.gov/authorities/subjects/sh85067099 http://id.loc.gov/authorities/subjects/sh93006704 http://id.loc.gov/authorities/subjects/sh97002073 |
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 | Fuzzy sets. http://id.loc.gov/authorities/subjects/sh85052627 Integrals. http://id.loc.gov/authorities/subjects/sh85067099 Fuzzy logic. http://id.loc.gov/authorities/subjects/sh93006704 Data mining. http://id.loc.gov/authorities/subjects/sh97002073 Ensembles flous. Intégrales. Logique floue. Exploration de données (Informatique) MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Data mining fast Fuzzy logic fast Fuzzy sets fast Integrals fast |
topic_facet | Fuzzy sets. Integrals. Fuzzy logic. Data mining. Ensembles flous. Intégrales. Logique floue. Exploration de données (Informatique) MATHEMATICS Infinity. MATHEMATICS Logic. Data mining Fuzzy logic Fuzzy sets Integrals |
url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374861 |
work_keys_str_mv | AT wangzhenyuan nonlinearintegralsandtheirapplicationsindatamining AT yangrong nonlinearintegralsandtheirapplicationsindatamining AT leungkwongsak nonlinearintegralsandtheirapplicationsindatamining |