Proportional transitivity in linear extensions of ordered sets
Journal of Combinatorial Theory Series B
Fuzzy Sets and Systems
A characterization of quasi-copulas
Journal of Multivariate Analysis
Transitivity of fuzzy preference relations—an empirical study
Fuzzy Sets and Systems
Bell-type inequalities in fuzzy probability calculus
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - Special issue on aggregation operators
A class of rational cardinality-based similarity measures
Journal of Computational and Applied Mathematics
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
Exploiting the Lattice of Ideals Representation of a Poset
Fundamenta Informaticae
On the transitivity of the comonotonic and countermonotonic comparison of random variables
Journal of Multivariate Analysis
On Representing and Generating Kernels by Fuzzy Equivalence Relations
The Journal of Machine Learning Research
On the transitivity of a parametric family of cardinality-based similarity measures
International Journal of Approximate Reasoning
Meta-theorems on inequalities for scalar fuzzy set cardinalities
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
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We present several relational frameworks for expressing similarities and preferences in a quantitative way. The main focus is on the occurrence of various types of transitivity in these frameworks. The first framework is that of fuzzy relations; the corresponding notion of transitivity is C-transitivity, with C a conjunctor. We discuss two approaches to the measurement of similarity of fuzzy sets: a logical approach based on biresidual operators and a cardinal approach based on fuzzy set cardinalities. The second framework is that of reciprocal relations; the corresponding notion of transitivity is cycle-transitivity. It plays a crucial role in the description of different types of transitivity arising in the comparison of (artificially coupled) random variables in terms of winning probabilities. It also embraces the study of mutual rank probability relations of partially ordered sets.