A relative tolerance relation of rough set with reduct and core approach, and application to incomplete information systems

Data mining concepts and methods can be applied in various fields. Many methods have been proposed and one of those methods is the classical 'rough set theory' which is used to analyze the complete data. However, the Rough Set classical theory cannot overcome the incomplete data. The simplest method for operating an incomplete data is removing unknown objects. Besides, the continuation of Rough Set theory is called tolerance relation which is less convincing decision in terms of approximation. As a result, a similarity relation is proposed to improve the results obtained through a tolerance relation technique. However, when applying the similarity relation, little information will be lost. Therefore, a limited tolerance relation has been introduced. However, little information will also be lost as limited tolerance relation does not take into account the accuracy of the similarity between the two objects. Hence, this study proposed a new method called Relative Tolerance Relation of Rough Set with Reduct and Core (RTRS) which is based on limited tolerance relation that takes into account relative similarity precision between two objects. Several incomplete datasets have been used for data classification and comparison of our approach with existing baseline approaches, such as the Tolerance Relation, Limited Tolerance Relation, and NonSymmetric Similarity Relations approaches are made based on two different scenarios. In the first scenario, the datasets are given the same weighting for all attributes. In the second scenario, each attribute is given a different weighting. Once the classification process is complete, the proposed approach will eliminate redundant attributes to develop an efficient reduce set and formulate the basic attribute specified in the incomplete information system. Several datasets have been tested and the rules generated from the proposes approach give better accuracy. Generally, the findings show that the RTRS method is better compared to the other methods as discussed in this study

NIS-Apriori-based rule generation with three-way decisions and its application system in SQL

In the study, non-deterministic information systems-Apriori-based (NIS-Apriori-based) rule generation from table data sets with incomplete information, SQL implementation, and the unique characteristics of the new framework are presented. Additionally, a few unsolved new research topics are proposed based on the framework. We follow the framework of NISs and propose certain rules and possible rules based on possible world semantics. Although each rule τ depends on a large number of possible tables, we prove that each rule τ is determined by examining only two τ -dependent possible tables. The NIS-Apriori algorithm is an adjusted Apriori algorithm that can handle such tables. Furthermore, it is logically sound and complete with regard to the rules. Subsequently, the implementation of the NIS-Apriori algorithm in SQL is described and a few new topics induced by effects of NIS-Apriori-based rule generation are confirmed. One of the topics that are considered is the possibility of estimating missing values via the obtained certain rules. The proposed methodology and the environment yielded by NIS-Apriori-based rule generation in SQL are useful for table data analysis with three-way decisions