Similarity relations, fuzzy partitions, and fuzzy orderings
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy preference structures without incomparability
Fuzzy Sets and Systems
Fuzzy Sets and Systems
A characterization of quasi-copulas
Journal of Multivariate Analysis
Fuzzy Sets and Systems
Domination of aggregation operators and preservation of transitivity
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Additive decomposition of fuzzy pre-orders
Fuzzy Sets and Systems
On the compositional characterization of complete fuzzy pre-orders
Fuzzy Sets and Systems
Meta-theorems on inequalities for scalar fuzzy set cardinalities
Fuzzy Sets and Systems
On the transitivity of fuzzy indifference relations
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
Transitivity Bounds in Additive Fuzzy Preference Structures
IEEE Transactions on Fuzzy Systems
The role of fuzzy sets in decision sciences: Old techniques and new directions
Fuzzy Sets and Systems
A study on the transitivity of probabilistic and fuzzy relations
Fuzzy Sets and Systems
On some properties of the negative transitivity obtained from transitivity
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
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We study the transitivity of fuzzy preference relations, often considered as a fundamental property providing coherence to a decision process. We consider the transitivity of fuzzy relations w.r.t. conjunctors, a general class of binary operations on the unit interval encompassing the class of triangular norms usually considered for this purpose. Having fixed the transitivity of a large preference relation w.r.t. such a conjunctor, we investigate the transitivity of the strict preference and indifference relations of any fuzzy preference structure generated from this large preference relation by means of an (indifference) generator. This study leads to the discovery of two families of conjunctors providing a full characterization of this transitivity. Although the expressions of these conjunctors appear to be quite cumbersome, they reduce to more readily used analytical expressions when we focus our attention on the particular case when the transitivity of the large preference relation is expressed w.r.t. one of the three basic triangular norms (the minimum, the product and the 驴ukasiewicz triangular norm) while at the same time the generator used for decomposing this large preference relation is also one of these triangular norms. During our discourse, we pay ample attention to the Frank family of triangular norms/copulas.