CP-nets的代数表示及其模型求取算法

Algebraic Representation and Model Solving Algorithm for CP-nets

条件偏好网(CP-nets)是一种表示定性条件偏好关系的语言.针对目前CP-nets的图形表示方法难以实现运算的特点提出一种二值无环CP-nets的代数表示方法.该方法将CP-nets组织成邻接链表的形式,纵向存储CP-nets拓扑排序的序列,其结点域以命题逻辑的主析取范式来表示二值CP-nets的条件偏好表.横向存储各个顶点的父亲集,它对应决策属性的条件集.随后基于CP-nets的代数表示方法,研究二值无环CP-nets上的直接模型和间接模型的求取算法.实验结果表明,CP-nets不仅能用直观的图形来表示,也可用紧凑的代数方法来表示.

Conditional preference networks （CP-nets）is a popular language which represents qualitative conditional preference relation. Aiming at the problem that graphical representation is not enough to fulfill operations on CP-nets, an algebraic representation of CP-nets is offered with the well-known adjacent list approach. In the approach, vertical nodes are organized organized by topological order, and horizontal nodes are by their parents. Particularly, conditional preference table of nodes are represented by main disjunctive normal form of proposition logic. A direct model solving algorithm is devised later, and an indirect model solving algorithm is gotten based on relation operation on direct model. In short, the representation approach reveals that CP-nets can be not only represented by simple and intuitive graphical approach, but also represented by compacted algebraic approach.