基于二元关系和布尔推理的分级决策模型

分级决策问题是将备选方案分类到预先定义的具有偏好顺序的决策类中.其中每个方案是由一个有限属性集合来描述的,该属性集合包括名义属性、连续型属性和有序属性.为了建立分级决策模型.提出了一种基于粗集理论和二元关系、布尔推理相结合的方法.首先在名义属性、连续型属性和有序属性上分别定义了不可分辨关系、相似关系和优势关系.然后提出了分辨-相似-支配矩阵的概念来建立相应的布尔函数.通过计算布尔函数的主蕴含,得到了"IF…THEN…"分级决策规则集作为偏好模型.最后利用一个算例说明了该方法的有用性.

Sorting decision model based on binary relations and Boolean reasoning

Sorting decision problems consist in assigning some alternatives into some pre-defined and preference-ordered decision classes.The ahematives are described by a finite set of attributes involving nominal attributes,continuous-valued attributes and ordinal attributes.In order to construct a comprehensive preference model used to support the sorting task,a method is proposed based on the combination of rough sets theory,binary relations and Boolean reasoning.Three binary relations including indiscernibility relation,similarity relation and outranking relation ale defined on nominal attributes,continuous-valued attributes and ordinal attributes,respectively.Then,a discernibilitysimilarity-dominance matrix is defined to construct the Boolean functions.The preference model,Boolean functions.The usefulness of this approach is illustrated with an example.