Much evidence suggests that a preference relation of a decision maker is often not transitive in reality. Armstrong [1, 2, 3] and Luce [11] argued that, in contrast to the standard utility theory, a preference relation of a decision maker is suffered from nontransitive indifferences due to the imperfect powers of discrimination. Kahneman and Tversky [8] presented the extensive experimental resu...

This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation ≺. They are equivalent to Shoham’s so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After ...

In this paper we investigate the problem of learning a preference relation i~om a given set of ranked documents. We show that the Bayes’s optimal decision function, when applied to learning a preference relation, may violate transitivity. This is undesirable for information retrieval, because it is in conflict with a document ranking based on the user’s preferences. To overcome this problem we ...

In [3] we presented a fuzzy multipurpose decision making model integrating different preference representations: preference orderings, utility functions and fuzzy preference relations. We complete the decision model studying its internal consistency.