Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets

The existing construction methods of granularity importance degree only consider the direct influence of single granularity on decision-making; however, they ignore the joint impact from other granularities when carrying out granularity selection. In this regard, we have the following improvements. First of all, we define a more reasonable granularity importance degree calculating method among multiple granularities to deal with the above problem and give a granularity reduction algorithm based on this method. Besides, this paper combines the reduction sets of optimistic and pessimistic multi-granulation rough sets with intuitionistic fuzzy sets, respectively, and their related properties are shown synchronously. Based on this, to further reduce the redundant objects in each granularity of reduction sets, four novel kinds of three-way decisions models with multi-granulation rough intuitionistic fuzzy sets are developed. Moreover, a series of concrete examples can demonstrate that these joint models not only can remove the redundant objects inside each granularity of the reduction sets, but also can generate much suitable granularity selection results using the designed comprehensive score function and comprehensive accuracy function of granularities.

A Novel Variable Precision Reduction Approach to Comprehensive Knowledge Systems

A comprehensive knowledge system reveals the intangible insights hidden in an information system by integrating information from multiple data sources in a synthetical manner. In this paper, we present a variable precision reduction theory, underpinned by two new concepts: 1) distribution tables and 2) genealogical binary trees. Sufficient and necessary conditions to extract comprehensive knowledge from a given information system are also presented and proven. A complete variable precision reduction algorithm is proposed, in which we introduce four important strategies, namely, distribution table abstracting, attribute rank dynamic updating, hierarchical binary classifying, and genealogical tree pruning. The completeness of our algorithm is proven theoretically and its superiority to existing methods for obtaining complete reducts is demonstrated experimentally. Finally, having obtaining the complete reduct set, we demonstrate how the relationships between the complete reduct set and the comprehensive knowledge system can be visualized in a double-layer lattice structure using Hasse diagrams.

Space Structure and Clustering of Categorical Data

Learning from categorical data plays a fundamental role in such areas as pattern recognition, machine learning, data mining, and knowledge discovery. To effectively discover the group structure inherent in a set of categorical objects, many categorical clustering algorithms have been developed in the literature, among which k -modes-type algorithms are very representative because of their good performance. Nevertheless, there is still much room for improving their clustering performance in comparison with the clustering algorithms for the numeric data. This may arise from the fact that the categorical data lack a clear space structure as that of the numeric data. To address this issue, we propose, in this paper, a novel data-representation scheme for the categorical data, which maps a set of categorical objects into a Euclidean space. Based on the data-representation scheme, a general framework for space structure based categorical clustering algorithms (SBC) is designed. This framework together with the applications of two kinds of dissimilarities leads two versions of the SBC-type algorithms. To verify the performance of the SBC-type algorithms, we employ as references four representative algorithms of the k -modes-type algorithms. Experiments show that the proposed SBC-type algorithms significantly outperform the k -modes-type algorithms.