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.
이 논문은 의사 결정자에의해 주어지는 각 대안들 간의 비교의 결과에 대한 분석적인 연구를 통해서 비이행적 비교의 구조에 대한 체계적인 이해를 돕고 나아가서는 이러한 분석을 통해 비이행적인 비교로부터 가장 근사한 이행적 비교의 결과를 얻을 수 있는 방법을 제시하고 있다. 기존의 방법과 비교하여 제시된 방법의 우수함도 역시 논의되고 있다.
