Granularity and Entropy of Intuitionistic Fuzzy Information and Their Applications

A granular structure of intuitionistic fuzzy (IF) information presents simultaneously the similarity and diversity of samples. However, this structural representation has rarely displayed its technical capability in data mining and information processing due to the lack of suitable constructive methods and semantic interpretation for IF information with regard to real data. To pursue better performance of the IF-based technique in real-world data mining, in this article, we examine information granularity, information entropy of IF granular structures, and their applications to data reduction of IF information systems. First, several types of partial-order relations at different hierarchical levels are defined to reveal the granularity of IF granular structures. Second, the granularity invariance between different IF granular structures is characterized by using relational mappings. Third, Shannon's entropies are generalized to IF entropies and their relationships with the partial-order relations are addressed. Based on the theoretical analysis above, the significance of intuitionistic attributes using the information measures is then introduced and the information-preserving algorithm for data reduction of IF information systems is constructed. Finally, by inducing substantial IF relations from public datasets that take both the similarity/diversity between the samples from the same/different classes into account, a collection of numerical experiments is conducted to confirm the performance of the proposed technique.

Information structures in a fuzzy β-covering information system

This paper studies information structures in a fuzzy β-covering information system. We introduce the concepts of a fuzzy β-covering information system and homomorphism between them, and investigate related properties. The concept of information structure of a fuzzy β-covering information system is given. We discuss the relationships between information structures from the view of dependence and separation. Then granularity measures for a fuzzy β-covering information system are studied. Finally, we discuss invariance of fuzzy β-covering information systems under homomorphism and illustrate its application on data compression.

Survey on granularity clustering

With the rapid development of uncertain artificial intelligent and the arrival of big data era, conventional clustering analysis and granular computing fail to satisfy the requirements of intelligent information processing in this new case. There is the essential relationship between granular computing and clustering analysis, so some researchers try to combine granular computing with clustering analysis. In the idea of granularity, the researchers expand the researches in clustering analysis and look for the best clustering results with the help of the basic theories and methods of granular computing. Granularity clustering method which is proposed and studied has attracted more and more attention. This paper firstly summarizes the background of granularity clustering and the intrinsic connection between granular computing and clustering analysis, and then mainly reviews the research status and various methods of granularity clustering. Finally, we analyze existing problem and propose further research.

A granular reflex fuzzy min-max neural network for classification

Granular data classification and clustering is an upcoming and important issue in the field of pattern recognition. Conventionally, computing is thought to be manipulation of numbers or symbols. However, human recognition capabilities are based on ability to process nonnumeric clumps of information (information granules) in addition to individual numeric values. This paper proposes a granular neural network (GNN) called granular reflex fuzzy min-max neural network (GrRFMN) which can learn and classify granular data. GrRFMN uses hyperbox fuzzy set to represent granular data. Its architecture consists of a reflex mechanism inspired from human brain to handle class overlaps. The network can be trained online using granular or point data. The neuron activation functions in GrRFMN are designed to tackle data of different granularity (size). This paper also addresses an issue to granulate the training data and learn from it. It is observed that such a preprocessing of data can improve performance of a classifier. Experimental results on real data sets show that the proposed GrRFMN can classify granules of different granularity more correctly. Results are compared with general fuzzy min-max neural network (GFMN) proposed by Gabrys and Bargiela and with some classical methods.