Three-way Decision Model Based On Local Rough Set

In order to study the rules of decision on the classification of objects in the domain,Yao proposed the three-way decision theory based on rough set and probabilistic rough set.It is developed based on the traditional two-way decisions.The three domains of rough set or probabilistic rough set can be respectively recognized as the positive domain corresponding to the acceptance domain,the negative domain corresponding to the rejection region,and the boundary domain corresponding to the disclaimer region(i.e.delaying to take decision).At present,the three-way decisions based on the different rough sets are widely studied and extended by many scholars,and they are applied in many fields.Based on rough set and probabilistic rough set,in this paper we study the probabilistic rough on the basis of the serial binary relation and the local rough set on the basis of the include degree and their relation properties.The three-way decision models and the classification decision rules under two models are given.The main research work of this paper is as follows:The first chapter of this paper introduces the background and significance of rough set theory and three-way decision theory,and the developments of them.In the second part of the paper,the basic notions and related properties of rough set and probabilistic rough set models are introduced.Chapter three produces the probabilistic rough set model based on a serial binary relation.The classical probabilistic rough set model is proposed based on an equivalence relation by Yao.In practical application,however,there are uncertain factors in knowledge base,which makes a binary relation between any two objects difficult to be equivalent.In order to resolve this question,and make the conditional probability meaningful,serial probabilistic rough set approximations are introduced on the basis of a serial binary relation.Meanwhile,the rough approximation of the corresponding serial probability lower and upper approximations,the serial probability precision and the serial probability roughness are also discussed as the two thresholds change.Finally,the three-way decision models of serial probabilistic rough set are investigated based on Bayesian decision and the conditional probability.Last chapter constructs the local rough set based on the inconsistent decision table.Theprobabilistic rough set model is based on the conditional probability,however,local rough set is put forward on the basis of the inclusion degree.First of all,according to the definitions of the local upper and lower approximations of local rough set,we give the definition of three local regions and their properties.As the two thresholds increasing or decreasing,the rough approximations of the local upper and lower approximations and the local boundary region of local rough set are discussed.Secondly,the local rough set model of the inconsistent decision table is given,and its attribute reductions are then discussed.Finally,three-way decision models based on the local rough set are introduced,and the corresponding decision rules for classification are shown.