Systematization of Choice Rules with Binary Relations

Abstract

Let us suppose that R is a binary preference relation on a finite set X of initial crisp alternatives; for x, y in X, xRy means “x is preferred to y”, For the above-stated reasons, no special a priori properties of R (transitivity, antisymmetry, weak completeness, etc.) are required. The problem is to determine, on the basis of R, ranking of X or at least the “subset of best alternatives”.