General transitivity conditions for fuzzy reciprocal preference matrices
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Cycle-transitive comparison of independent random variables
Journal of Multivariate Analysis
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
On the transitivity of the comonotonic and countermonotonic comparison of random variables
Journal of Multivariate Analysis
On the cycle-transitive comparison of artificially coupled random variables
International Journal of Approximate Reasoning
IEEE Transactions on Fuzzy Systems
Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity
Fuzzy Sets and Systems
General results on the decomposition of transitive fuzzy relations
Fuzzy Optimization and Decision Making
Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Transitivity Bounds in Additive Fuzzy Preference Structures
IEEE Transactions on Fuzzy Systems
A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations
IEEE Transactions on Fuzzy Systems
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Given a set of alternatives we consider a fuzzy relation and a probabilistic relation defined on such a set. We investigate the relation between the T-transitivity of the fuzzy relation and the cycle-transitivity of the associated probabilistic relation. We provide a general result, valid for any t-norm and we later provide explicit expressions for important particular cases. We also apply the results obtained to explore the transitivity satisfied by the probabilistic relation defined on a set of random variables. We focus on uniform continuous random variables.