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Title: Bell-type inequalities for parametric families of triangular norms (English)
Author: Janssens, Saskia
Author: De Baets, Bernard
Author: De Meyer, Hans
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 40
Issue: 1
Year: 2004
Pages: [89]-106
Summary lang: English
Category: math
Summary: In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities; second, for the most important parametric families of continuous Archimedean t-norms and each of the inequalities, we identify the parameter values such that the corresponding t-norms satisfy the inequality considered. (English)
Keyword: Bell inequality
Keyword: fuzzy set
Keyword: quasi-copula
Keyword: triangular norm
MSC: 03E72
MSC: 06F05
MSC: 54A25
MSC: 54A40
idZBL: Zbl 1249.54015
idMR: MR2068600
Date available: 2009-09-24T19:59:39Z
Last updated: 2015-03-23
Stable URL:
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