基于知识距离的粗糙粒结构的评价模型

Evaluation model of rough granular structure based on knowledge distance

在粒计算理论中,通过不同的粒计算机制可以生成不同的粒结构。在粗糙集中,对于同一个信息表而言,通过不同的属性添加顺序可以得到由不同的序贯层次结构,即粗糙粒结构。在粗糙粒结构中,不同的属性获取顺序导致了对不确定性问题求解的不同程度。因此,如何有效评价粗糙粒结构是一个值得研究的问题。本文将从知识距离的角度研究这个问题。首先,在前期工作所提出的知识距离框架上提出了一种粗糙近似空间距离,用于度量粗糙近似空间之间差异性。基于提出的知识距离,研究了粗糙粒结构的结构特征。在粗糙粒结构中,在对不确定性问题进行求解时,本文希望在约束条件下可以利用尽可能少的知识空间使不确定性降低达到最大化。基于这个思想并利用以上得出的结论,在属性代价约束条件下,引入了一个评价参数λ,并在此基础建立了一种粗糙粒结构的评价模型,该方法实现了在属性代价约束条件下选择粗糙粒结构的功能。最后,通过实例验证了本文提出的模型的有效性。

In the theory of granular computing(GrC),different granular structures are generated by various grain calculation mechanisms.In rough sets,for the same information table,different attribute adding sequence produces different sequential hierarchical structure,namely the rough granular structure.In rough granular structure,various order of attribute acquisition leads to different effects of solving uncertain problems.This leads to an interesting research topic:how to effectively evaluate the rough granular structures.This problem is solved from the perspective of knowledge distance in the paper.Firstly,the knowledge distance mentioned in our previous works is introduced and then a rough approximation space distance(RASD)is proposed to measure the difference between rough approximate space.On the basis of the knowledge distance mentioned above,the characteristic of rough granular structure(RGS)is investigated.In the rough granular structure,when solving uncertain problem,we expect to to maximize the uncertainty reduction as much as possible by using smaller knowledge space.Then,based on this idea and the above conclusions,an evaluation parameterλis introduced under the constraint of attribute cost,and further,an evaluation model of rough granular structure is established.This achieves a way to select the rough granular structure according to the constraint.Finally,the effectiveness of this method is verified by an example.