LEADER 00000cam a2200709Ia 4500 001 ocn182537640 003 OCoLC 005 20160527041200.7 006 m o d 007 cr cnu---unuuu 008 071127s2006 njua ob 001 0 eng d 019 815749966 020 9789812774200|q(electronic book) 020 9812774203|q(electronic book) 020 1281919349 020 9781281919342 035 (OCoLC)182537640|z(OCoLC)815749966 040 N$T|beng|epn|cN$T|dYDXCP|dOCLCQ|dIDEBK|dOCLCQ|dOCLCO |dNLGGC|dOCLCQ|dSTF|dOCLCQ 049 RIDW 050 4 QA431|b.A52 2006eb 072 7 MAT|x037000|2bisacsh 072 7 GPFC|2bicssc 082 04 515/.7|222 090 QA431|b.A52 2006eb 100 1 Alsina, Claudi.|0https://id.loc.gov/authorities/names/ n79030525 245 10 Associative functions :|btriangular norms and copulas / |cClaudi Alsina, Maurice J. Frank, Berthold Schweizer. 264 1 Hackensack, NJ :|bWorld Scientific,|c[2006] 264 4 |c©2006 300 1 online resource (xiv, 237 pages) :|billustrations 336 text|btxt|2rdacontent 337 computer|bc|2rdamedia 338 online resource|bcr|2rdacarrier 340 |gpolychrome|2rdacc 347 text file|2rdaft 504 Includes bibliographical references (pages 223-234) and index. 505 0 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. 520 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. 588 0 Print version record. 590 eBooks on EBSCOhost|bEBSCO eBook Subscription Academic Collection - North America 650 0 Functional equations.|0https://id.loc.gov/authorities/ subjects/sh85052317 650 0 Associative law (Mathematics)|0https://id.loc.gov/ authorities/subjects/sh85008822 650 0 Mathematical analysis.|0https://id.loc.gov/authorities/ subjects/sh85082116 650 0 Functional equations|0https://id.loc.gov/authorities/ subjects/sh85052317|xStudy and teaching|0https:// id.loc.gov/authorities/subjects/sh2001008697|vTextbooks. |0https://id.loc.gov/authorities/subjects/sh99001753 650 0 Associative law (Mathematics)|0https://id.loc.gov/ authorities/subjects/sh85008822|xStudy and teaching|0https ://id.loc.gov/authorities/subjects/sh2001008697 |vTextbooks.|0https://id.loc.gov/authorities/subjects/ sh99001753 650 0 Mathematical analysis|0https://id.loc.gov/authorities/ subjects/sh85082116|xStudy and teaching|0https:// id.loc.gov/authorities/subjects/sh2001008697|vTextbooks. |0https://id.loc.gov/authorities/subjects/sh99001753 650 7 Functional equations.|2fast|0https://id.worldcat.org/fast/ 936067 650 7 Associative law (Mathematics)|2fast|0https:// id.worldcat.org/fast/819228 650 7 Mathematical analysis.|2fast|0https://id.worldcat.org/fast /1012068 650 7 Mathematical analysis|xStudy and teaching.|2fast|0https:// id.worldcat.org/fast/1012074 655 4 Electronic books. 655 7 Textbooks.|2fast|0https://id.worldcat.org/fast/1423863 655 7 Textbooks.|2lcgft|0https://id.loc.gov/authorities/ genreForms/gf2014026191 700 1 Schweizer, B.|q(Berthold)|0https://id.loc.gov/authorities/ names/n81145090 700 1 Frank, Maurice J.|0https://id.loc.gov/authorities/names/ no2006086057 776 08 |iPrint version:|aAlsina, Claudi.|tAssociative functions. |dHackensack, NJ : World Scientific, ©2006|z9812566716 |z9789812566713|w(DLC) 2006284938|w(OCoLC)76144355 856 40 |uhttps://rider.idm.oclc.org/login?url=http:// search.ebscohost.com/login.aspx?direct=true&scope=site& db=nlebk&AN=210845|zOnline eBook. 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