Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
Fuzzy preference structures without incomparability
Fuzzy Sets and Systems
A characterization of quasi-copulas
Journal of Multivariate Analysis
Gödel representable fuzzy weak orders
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Fuzzy Sets and Systems
A compendium of fuzzy weak orders: Representations and constructions
Fuzzy Sets and Systems
Additive decomposition of fuzzy pre-orders
Fuzzy Sets and Systems
On the structure of left-continuous t-norms that have a continuous contour line
Fuzzy Sets and Systems
On the transitivity of a parametric family of cardinality-based similarity measures
International Journal of Approximate Reasoning
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
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
An Introduction to Copulas
A top-down algorithm for generating the Hasse tree of a fuzzy preorder closure
IEEE Transactions on Fuzzy Systems
Transitivity Bounds in Additive Fuzzy Preference Structures
IEEE Transactions on Fuzzy Systems
Modeling rationality in a linguistic framework
Fuzzy Sets and Systems
General results on the decomposition of transitive fuzzy relations
Fuzzy Optimization and Decision Making
Quasi-copulas and signed measures
Fuzzy Sets and Systems
The role of fuzzy sets in decision sciences: Old techniques and new directions
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
Collective transitivity in majorities based on difference in support
Fuzzy Sets and Systems
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Complete pre-orders can be characterized in terms of the transitivity of the corresponding strict preference and indifference relations. In this paper, we investigate this characterization in a fuzzy setting. We consider two types of completeness (weak completeness and strong completeness) and decompose a fuzzy pre-order by means of an indifference generator, in particular a Frank t-norm. In the weakly complete case, we identify the strongest type of transitivity of the indifference and strict preference relations in function of the generator used for constructing them. In the strongly complete case, we lay bare a stronger type of transitivity of the strict preference relation. We conclude the paper with a rather negative result: there is no hope to obtain a compositional characterization of weakly complete fuzzy pre-orders, and hence also not of fuzzy pre-orders in general.