Inequalities in fuzzy probability calculus

Authors:
Saskia Janssens;Bernard De Baets;Hans De Meyer
Affiliations:
Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Gent, Belgium;Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Gent, Belgium;Department of Applied Mathematics and Computer Science Ghent University, Krijgslaan, Gent, Belgium
Venue:
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
Year:
2003

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Abstract

We present all Bell-type inequalities concerning at most four random events of which not more than two are intersected at the same time. Reformulating these inequalities in the context of fuzzy probability calculus leads to related inequalities on commutative conjunctors, and in particular on triangular norms and commutative copulas. For the most important parametric families of t-norms, we identify the parameter values for which each of the inequalities is fulfilled. Some of the inequalities hold for any commutative copula, while all of them are preserved under ordinal sums.