Abstract
For crisp relations the transitivity of a relation and the negative transitivity of its dual are equivalent conditions. Particularly, a crisp complete large preference relation is transitive if and only if its associated strict preference relation is negatively transitive. In this contribution we focus on one of those implications for fuzzy relations. Recall that in the context of fuzzy relations there are multiple ways of obtaining the strict preference relation from the large preference relation, and also multiple ways for defining transitivity. We analyze the type of negative transitivity we can assure for the strict preference relation, departing from a large preference relation that satisfies almost any kind of transitivity. We recall the general expression we obtained and study some interesting properties. Finally, we pay special attention to the particular case of the minimum t-norm both in the role of generator and in the role of conjunctor defining the transitivity of the original reflexive relation.
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Díaz, S., Montes, S., De Baets, B. (2012). On Some Properties of the Negative Transitivity Obtained from Transitivity. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_28
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DOI: https://doi.org/10.1007/978-3-642-34620-0_28
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