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Bell-type inequalities for parametric families of triangular norms. (English) Zbl 1249.54015
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.

##### MSC:
 54A40 Fuzzy topology 06F05 Ordered semigroups and monoids 03E72 Theory of fuzzy sets, etc.
##### Keywords:
Bell inequality; fuzzy set; quasi-copula; triangular norm
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##### References:
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