Kybernetika 40 no. 1, 89-106, 2004

Bell-type inequalities for parametric families of triangular norms

Saskia Janssens, Bernard De Baets and Hans De Meyer


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.