Research On Dynamic Update Method Of Approx Imations For Multi-granulation Rough Sets

Polish mathematician Pawlak proposed a mathematical tool for dealing with fuzzy knowledge in 1982,namely rough set theory.The classical rough set uses the single indistinguishable binary relation on the domain to derive the equivalence class,and calculates the upper approximations and the lower approximations by discussing the relationship between the equivalence class and the target concept.Granular computing is a fast-growing emerging discipline.Word computing model,rough set model and quotient space model are three main granular computing models.At present,rough set theory has become an important model tool for studying granular computing.From the perspective of granular computing,the classical rough set is a single-level,single-grained granular computing model,which cannot analyze and deal with problems from multiple levels and multiple granularities.Therefore,according to the idea of granular computing,Qian Yuhua et al.proposed a multi-granulation rough set model based on complete information system.At present,with the rapid development of information technology,the data in the information system will change with time.It can be seen that the knowledge of multi-granulation rough set will also change dynamically.The researchers have proposed many dynamic update algorithms for knowledge acquisition for rough set model and its extended model.However,most of the proposed dynamic update algorithms are based on the single-granulation rough set model.It is discussed how to update the approximations when the data changes in the complete information system,but the approximations in the multi-granulation rough set and its extended model.There are few studies on the dynamic update algorithm,and in some studies,the approximations dynamic update algorithm is less efficient.In the existing information system,due to the loss of information records or the mistakes in collecting information,the information to be processed may contain missing values.Therefore,when scholars want to acquire knowledge,it is often necessary to process an information system with incomplete attribute values.When data changes in an incomplete information system,it will be more complicated than a complete information system because it contains missing values.When an incomplete information system changes,it is difficult to deal with common multi-granulation rough set models.Therefore,few scholars have studied the approximations dynamic update algorithm under incomplete information systems.For the above two problems,this paper takes the complete information system and the incomplete information system as the research basis,and discusses the following two aspects:(1)In the multi-granulation rough set environment,when the attribute values in the complete information system are refined,the original approximations will change,that is,the lower approximations has a tendency to become larger,and the upper approximations has a smaller trend,and The existing approximations update algorithm has low time efficiency,and the improvement of the existing approximations dynamic update algorithm has become an important content in the research of multi-granulation rough set theory.For this reason,in the multi-granulation environment,the relevance properties and theorems of dynamic update of optimistic and pessimistic multi-granulation rough set approximations are discussed for the case where the attribute values in the information system are refined.The approximations dynamic update algorithm is proposed.The basic idea of the algorithm is that it does not need to recalculate the equivalence class of the object in the information system when refining the attribute value.It is only necessary to calculate the approximations according to whether the attribute values in different local ranges in the domain are not equal,that is,update the approximations according to the inequality class of the object.Finally,a large number of experiments are carried out in the UCI public data set.The experimental results show that the proposed algorithm is better than the comparison algorithm in updating the approximations time efficiency,which verif-ies the correctness and efficiency of the proposed algorithm.(2)For the problem that the missing value may be obtained when the incomplete information system changes,in order to solve the problem of low time efficiency when updating the approximations in the multi-granulation rough set,a dynamic update approximations algorithm based on the tolerance relationship is proposed.Firstly,the properties of the approximations change based on the tolerance relationship are discussed,and the trend of the optimistic and pessimistic multi-granulation rough set approximations is obtained according to the relevant properties.Then,for the problem of updating the tolerance class with low time efficiency,the theorem of dynamic update tolerance class is proposed.By using this theorem to dynamically update the tolerance class,the time to update the approximations is shorter.Based on this,a dynamic update approximations algorithm based on tolerance relationship is designed.Simulation experiments are carried out using four data sets in the UCI database.When the data set becomes larger,the calculation time difference between the proposed algorithm and the static algorithm is also larger.The experiment shows that the dynamic algorithm is more efficient than the static algorithm,which shows the correctness and efficiency of the proposed dynamic algorithm.