Rules Acquisition And Attribute Reduction Of D-type Probabilistic Formal Decision Context

The formal context is the basic data form in formal concept analysis.It shows the binary relation between objects and attributes.Formal decision context is a special kind of formal context which contains condition attributes and decision attributes.Rules acquisition and attribute reduction are two important research directions on the basis of formal decision context.In this paper,the D-type probabilistic formal decision context is proposed to solve the problem of uncertainty decision-making in our daily life.Then,the consistence of D-type probability decision formal context is defined.Based on the consistent D-type probability formal decision context,the acquisition of decision rules and attribute reduction to preserve decision rules relatively optimal are also studied.The main contents of this paper are as follows:1.Based on uncertainty decision-making problems,D-type probabilistic formal decision context is proposed and a new operator is defined on it.Then the probabilistic concepts are obtained and the corresponding concept lattice is constructed.We also discuss the properties of this new kind of decision context.Then,using the inclusion degree,we define the consistence of D-type probability formal decision context.And we study the rules acquisition on the a consistent D-type probability formal decision context.2.The attribute reduction to preserve decision rules relatively optimal is studied,which makes the rule more simple and compact.Further more,the attribute reduction to preserve non-redundant decision rules relatively optimal is studied.3.Three kinds of relationships are discussed in this paper.The first one is the relationship between probability concept lattice and the classic concept lattice.The second one is the relationship between lattice preserved attribute reduction and attribute reduction to preserve decision rules relatively optimal.The last one is the relationship between consistent set to preserve decision rules relatively optimal and consistent set to preserve non-redundant decision rules relatively optimal.