Abstract
Intransitive preference relation is often observed, when a multi-attribute preference is involved in decisions. To handle these cases, it becomes necessary to express the preference function which preserves the intransitive preference relation in terms of the single-attribute preference functions. This is called the decomposition of preference function.
This study is to investigate the necessary and the sufficient conditions for the various types of the decomposition of preference functions. Decomposable structure, difference structure and additive difference structure are examined along with the concepts of preference independence, Parato preference and restricted transitivity each of which plays an important role in the nacessary and the sufficient conditions for these structures.
Two types of intransitive preference relation so far proposed are shown to be described by the additive difference structure, the condition that the additive difference structure is to be transitive is given and the rate of the intransitive preference in the additive difference structure is computed through the probabilistic simulation.
