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Associative Functions: Triangular Norms And Copulas

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Title: Associative Functions: Triangular Norms And Copulas
Description: The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the “triangular norms” introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis.This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.
Authors: Claudi Alsina, Frank Maurice, Berthold Schweizer
Resource Type: eBook.
Subjects: Functional equations--Study and teaching--Textbooks, Associative law (Mathematics)--Study and teaching--Textbooks, Mathematical analysis--Study and teaching--Textbooks, Functional equations, Associative law (Mathematics), Mathematical analysis
Categories: MATHEMATICS / Differential Equations / General
Database: eBook Collection (EBSCOhost)
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PubType: eBook
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  Data: Associative Functions: Triangular Norms And Copulas
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  Data: The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the “triangular norms” introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis.This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.
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  Data: <searchLink fieldCode="AR" term="%22Claudi+Alsina%22">Claudi Alsina</searchLink><br /><searchLink fieldCode="AR" term="%22Frank+Maurice%22">Frank Maurice</searchLink><br /><searchLink fieldCode="AR" term="%22Berthold+Schweizer%22">Berthold Schweizer</searchLink>
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RecordInfo BibRecord:
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      – Code: 515.7
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Functional equations--Study and teaching--Textbooks
        Type: general
      – SubjectFull: Associative law (Mathematics)--Study and teaching--Textbooks
        Type: general
      – SubjectFull: Mathematical analysis--Study and teaching--Textbooks
        Type: general
      – SubjectFull: Functional equations
        Type: general
      – SubjectFull: Associative law (Mathematics)
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
    Titles:
      – TitleFull: Associative Functions: Triangular Norms And Copulas
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Claudi Alsina
      – PersonEntity:
          Name:
            NameFull: Frank Maurice
      – PersonEntity:
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            NameFull: Berthold Schweizer
      – PersonEntity:
          Name:
            NameFull: Claudi Alsina
      – PersonEntity:
          Name:
            NameFull: Frank Maurice
      – PersonEntity:
          Name:
            NameFull: Berthold Schweizer
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2006
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9789812566713
            – Type: isbn-electronic
              Value: 9789812774200
          Titles:
            – TitleFull: Associative Functions: Triangular Norms And Copulas
              Type: main
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