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|a QA431
|b .A52 2006eb
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|a HCDD
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|a Alsina, Claudi.
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|a Associative functions :
|b triangular norms and copulas /
|c Claudi Alsina, Maurice J. Frank, Berthold Schweizer.
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|a Singapore ;
|a Hackensack, NJ :
|b World Scientific,
|c ©2006.
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|a 1 online resource (xiv, 237 pages) :
|b illustrations
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 347 |
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|a data file
|2 rda
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|a Includes bibliographical references (pages 223-234) and index.
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|a Print version record.
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|a 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. Si.
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|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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|a English.
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|a Functional equations.
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| 650 |
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|a Associative law (Mathematics)
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|a Mathematical analysis.
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|a Functional equations
|x Study and teaching
|v Textbooks.
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|a Associative law (Mathematics)
|x Study and teaching
|v Textbooks.
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|a Mathematical analysis
|x Study and teaching
|v Textbooks.
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|a Associative law (Mathematics)
|2 fast
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| 650 |
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|a Functional equations
|2 fast
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|a Mathematical analysis
|2 fast
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|a Mathematical analysis
|x Study and teaching
|2 fast
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|a Textbooks
|2 fast
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|a Schweizer, B.
|q (Berthold)
|1 https://id.oclc.org/worldcat/entity/E39PCjGhwWqFBXTxXXmfmfQdHC
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|a Frank, Maurice J.
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|i Print version:
|a Alsina, Claudi.
|t Associative functions.
|d Singapore ; Hackensack, NJ : World Scientific, ©2006
|w (DLC) 2006284938
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| 856 |
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|u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=1681474
|y Click for online access
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|a EBC-AC
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|a 92
|b HCD
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