(A) study on the intransitive features of binary comparisons in a ranking problem

Abstract

Many traditional algebraic analyses of preference and choice for a finite set of alternatives have been based on binary choices. They have assumed that the binary preference information given by DM is transitive. However, there is considerable evidence that many relations that might occur as preference relations cannot be represented as transitive relations., We explore the basic structures of the transitive/intransitive binary comparisons under some assumptions. And we will also suggest a new concept which helps us understand the basic structures well, and suggest an efficient heuristic method to derive a transitive binary system from the intransitive one provided by a DM. Some merits of the suggested method over the existing methods are also discussed. Using the analyses given in this thesis, in the appendix, we provide an interactive graph display computer program, which helps a decision maker find a most preferred alternative among the available alternatives.