Decomposition of the Transitivity for Additive Fuzzy Preference Structures

Transitivity is a very important property in order to provide coherence to a preference relation. Usually, t-norms are considered to define the transitivity of fuzzy relations. In this paper we deal with conjunctors, a wider family than t-norm, to define the transitivity. This more general definition allows to impove the results found in the literature. We characterize the behaviour with respect to transitivity of the strict preference and indifference relations of any fuzzy preference structure associated to any large preference relation. Those two characterizations provide very general expressions. We also obtain easier expressions in some particular cases. Keywords— Fuzzy preference relation, transitivity, conjunctor, indifference generator.