ON THE IMPLEMENTATION OF PREFERENCE RELATIONAL SYSTEMS IN A COMPUTER-AIDED DECISION SUPPORT SYSTEM

Preference systems are models used in managing the preferences on a set of alternatives. Preference relational systems are preference systems based on a series of exhaustive and mutually exclusive binary relations. Preferences are best shown about paired comparisons, and binary relations are the most intuitive and suitable mathematical tool for modeling preferences based on paired comparisons. In addition to a preference relation P and an indifference relation I, a general preference relational system includes a semipreference relation S between the preference and an indifference and the incomparability relation X corresponding to the nonexistence of preference information to relate the alternatives. The system is simple when the semipreference is excluded and complete when the incomparability is excluded. The most important structures of these systems are introduced by mixed transitivity properties (conditions to infer a preference relation from a chain of related alternatives). The mixed transitivity is the most natural way to introduce the structures of the systems. These structures (the preorder, the semiorder, the interval order, the quasi-order, the double semiorder, and the pseudo-order) are characterized by essential implications (the simplest consequences of the mixed transitivities), by the properties of the functions in the value-threshold support, by the circuits in the graph representation, and by the shapes of the matrix representation. The value threshold and the graph and matrix representations are also useful for understanding them. In addition, the tools designed for the transitivity