A transitivity approach to preference relational systems

Preference relational systems are preference structures based on a series of exhaustive and mutually exclusive binary relations. The paper considers the most important types of these systems introduced from mixed transitivity properties, i.e., conditions under which a chain of preference and/or indifference relations implies the preference between the first and the last object in the chain. It analyzes the representation of these models by using graphs, matrices and value-threshold functions. The structure of the model is characterized by its representation when the incomparability is excluded.