Matroidal structure of generalized rough sets based on symmetric and transitive relations

Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and transitive relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and transitive relations, and provide an approach to study the matroid induced by a symmetric and transitive relation. Secondly, this paper establishes a close relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and transitive relation can be constructed by a matroid with some special properties.Comment: 5 page

Connectedness of graphs and its application to connected matroids through covering-based rough sets

Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and covering-based rough sets provide a systematic approach to this type of representation. In this paper, we study the connectedness of graphs through covering-based rough sets and apply it to connected matroids. First, we present an approach to inducing a covering by a graph, and then study the connectedness of the graph from the viewpoint of the covering approximation operators. Second, we construct a graph from a matroid, and find the matroid and the graph have the same connectedness, which makes us to use covering-based rough sets to study connected matroids. In summary, this paper provides a new approach to studying graph theory and matroid theory

Rough sets and matroidal contraction

Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to matroids and study the contraction of the dual of the corresponding matroid. First, for an equivalence relation on a universe, a matroidal structure of the rough set is established through the lower approximation operator. Second, the dual of the matroid and its properties such as independent sets, bases and rank function are investigated. Finally, the relationships between the contraction of the dual matroid to the complement of a single point set and the contraction of the dual matroid to the complement of the equivalence class of this point are studied.Comment: 11 page

A Data Preprocessing Algorithm for Classification Model Based On Rough Sets

AbstractAimed to solve the limitation of abundant data to constructing classification modeling in data mining, the paper proposed a novel effective preprocessing algorithm based on rough sets. Firstly, we construct the relation Information System using original data sets. Secondly, make use of attribute reduction theory of Rough sets to produce the Core of Information System. Core is the most important and necessary information which cannot reduce in original Information System. So it can get a same effect as original data sets to data analysis, and can construct classification modeling using it. Thirdly, construct indiscernibility matrix using reduced Information System, and finally, get the classification of original data sets. Compared to existing techniques, the developed algorithm enjoy following advantages: (1) avoiding the abundant data in follow-up data processing, and (2) avoiding large amount of computation in whole data mining process. (3) The results become more effective because of introducing the attributes reducing theory of Rough Sets

Encapsulation of Soft Computing Approaches within Itemset Mining a A Survey

Data Mining discovers patterns and trends by extracting knowledge from large databases. Soft Computing techniques such as fuzzy logic, neural networks, genetic algorithms, rough sets, etc. aims to reveal the tolerance for imprecision and uncertainty for achieving tractability, robustness and low-cost solutions. Fuzzy Logic and Rough sets are suitable for handling different types of uncertainty. Neural networks provide good learning and generalization. Genetic algorithms provide efficient search algorithms for selecting a model, from mixed media data. Data mining refers to information extraction while soft computing is used for information processing. For effective knowledge discovery from large databases, both Soft Computing and Data Mining can be merged. Association rule mining (ARM) and Itemset mining focus on finding most frequent item sets and corresponding association rules, extracting rare itemsets including temporal and fuzzy concepts in discovered patterns. This survey paper explores the usage of soft computing approaches in itemset utility mining

Rough sets for mining educational data

While educational data are typically analyzed with statistical software, data mining techniques are increasingly appropriate in revealing complex relationships among multiple variables in large amounts of data. We experimented with the rough set method in conjunction with statistical analysis to identify patterns in, and thereby extract meaning from, complex educational data. Results establish the benefits of combining rough set decision making with stochastic analysis in mining exceedingly complex and difficult to interpret educational data sets