Biorder families, valued relations and preference modelling
Journal of Mathematical Psychology
Transitivity of fuzzy preference relations—an empirical study
Fuzzy Sets and Systems
On the transitivity of the comonotonic and countermonotonic comparison of random variables
Journal of Multivariate Analysis
Optimal strategies for equal-sum dice games
Discrete Applied Mathematics
On the cycle-transitive comparison of artificially coupled random variables
International Journal of Approximate Reasoning
IEEE Transactions on Fuzzy Systems
The financial relevance of fuzzy stochastic dominance: a brief note
Fuzzy Sets and Systems
Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity
Fuzzy Sets and Systems
On the cycle-transitivity of the mutual rank probability relation of a poset
Fuzzy Sets and Systems
A transitivity analysis of bipartite rankings in pairwise multi-class classification
Information Sciences: an International Journal
On the ERA ranking representability of pairwise bipartite ranking functions
Artificial Intelligence
A study on the transitivity of probabilistic and fuzzy relations
Fuzzy Sets and Systems
The quest for transitivity, a showcase of fuzzy relational calculus
WCCI'12 Proceedings of the 2012 World Congress conference on Advances in Computational Intelligence
On a conjecture about the Frank copula family
Fuzzy Sets and Systems
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The discrete dice model, previously introduced by the present authors, essentially amounts to the pairwise comparison of a collection of independent discrete random variables that are uniformly distributed on finite integer multisets. This pairwise comparison results in a probabilistic relation that exhibits a particular type of transitivity, called dice-transitivity. In this paper, the discrete dice model is generalized with the purpose of pairwisely comparing independent discrete or continuous random variables with arbitrary probability distributions. It is shown that the probabilistic relation generated by a collection of arbitrary independent random variables is still dice-transitive. Interestingly, this probabilistic relation can be seen as a graded alternative to the concept of stochastic dominance. Furthermore, when the marginal distributions of the random variables belong to the same parametric family of distributions, the probabilistic relation exhibits interesting types of isostochastic transitivity, such as multiplicative transitivity. Finally, the probabilistic relation generated by a collection of independent normal random variables is proven to be moderately stochastic transitive.