不完备信息系统中的广义多粒度双相对定量决策粗糙集

Generalized multigranulation double-relative-quantitative decision-theoretic rough sets in incomplete information system

经典的粗糙集理论建立在等价关系基础上,要求过于严格,所以限制了它的实际应用范围.为此,扩展形式的粗糙集模型得到了广泛关注,并已成为研究热点.在现实世界中,由于数据测量的误差、对数据的理解或获取的限制等众多原因,所遇到的信息系统往往是不完备的.面向不完备信息系统,在广义多粒度粗糙集以及双相对定量决策粗糙集的基础上定义了两种广义多粒度双相对定量决策粗糙集(GMDrq-DTRS).一方面,讨论GMDrq-DTRS与广义多粒度粗糙集之间的等价关系,以及它们正负域的大小关系;另一方面,在不同的参数关系下,讨论GMDrqDTRS的正域、负域以及上下边界域所具有的特殊关系.并用具体实例来解释说明GMDrq-DTRS决策过程和所讨论的GMDrq-DTRS与其他模型之间的关系.

The classical rough set model is established on the base of an equivalence relation,and its requirement is too strict.In real life,the application of classical rough set theory has certain limitation.It is important for the development of rough set model by introducing other binary relations,which have become hot topics.In the real world,information acquisition systems suffer from the data measurement error,the understanding of the data and the limits of data acquisition,and information systems are usually incomplete.In order to address the relative and absolute information of the incomplete information system,this paper develops two generalized multigranulation double-relativequantitative decision-theoretic rough sets（GMDrq-DTRS）by combing generalized multigranulation decision-rough sets（GM-DTRS）and double-relative-quantitative decision rough sets（Drq-DTRS）.On the one hand,the equivalent relations between two GMDrq-DTRS and GM-DTRS and the relationship of size between their positive region and negative region are explored.On the other hand,the special relations between the positive region,negative region andboundary region of the first generalized multigranulation double-relative-quantitative decision-theoretic rough sets（GMDrq1-DTRS）and the second generalized multigranulation double-relative-quantitative decision-theoretic rough sets（GMDrq2-DTRS）are discussed under the influence of different parameters＇ relations.Finally,an illustrative example is employed to illustrate the decision process of GMDrq-DTRS established in the paper and show the relationships between GMDrq-DTRS and other rough set models by taking different parameters.