Research On Approximation Operator Based On Maximal Consistent Block And Its Application

Information system is a database with relationships between objects and attributes.Because of the diversity of database,the acquisition of knowledge depends on mathematical methods and calculation tools.The main research content of this thesis is to study attribute reduction on incomplete information system and multi-attribute group decision-making problems by using extended rough set model of maximum compatible block.The main work is as follows:(1)Attribute reduction of incomplete information system is studied.Firstly,optimistic and pessimistic generalized variable precision rough set models based on maximal consistent blocks are constructed,the relationship between the two models and their main properties are analyzed.After that ?-lower optimistic(pessimistic)and ?-upper distribution attribute reduction is defined,which keep the upper(lower)approximation distribution of the decision class unchanged.The corresponding judgement theorem is given,and Boolean method of the attribute reduction is obtained.This method of constructing discernibility set between maximal consistent blocks reduces the size of the discernibility matrix,and the process of computing attribute reduction is simplified,which can effectively save computing time and storage space.Then two examples of incomplete information systems with “lost”,“don't care” values and only “don't care” values are employed to illustrate the proposed method.Finally,5 incomplete information data sets from UCI data set are used to validate its effectiveness.(2)Multigranulation decision-theoretic rough set is proposed for decision-making in real life.In this paper,the classical multigranulation decision-theoretic rough sets are extended to the multigranulation decision-theoretic rough sets based on maximal consistent blocks,from the perspective of pessimistic and optimistic models.Four kinds of multigranulation decision rough sets based on maximal consistent blocks in the approximate space of multi-tolerance relations are defined and their properties are studied.After that,the relationships among these new approximation sets are obtained.Furthermore,the relationships between the new models and the existing models are developed.Finally,a case study to demonstrate the effectiveness of the proposed models is provided.(3)Using the variable precision maximal consistent blocks of rough set theory,a new method for multiple attribute group decision making is constructed.In a decision making information system,two kinds of variable precision rough set models based on maximal consistent blocks are defined,which are generated by a similar(compatible)relations from an attribute or a subset of attributes.The universe of discourse is divided into two disjoint parts of qualified set and unqualified set.Using the upper and lower approximations of the two sets,an optimal index function is defined,and a new sorting scheme is obtained.The results are extended to fuzzy environment,a decision-theoretic rough fuzzy set model based on maximal consistent blocks is proposed,which is then used for multiple attribute group decision making.