Publications

Anomaly (outlier) detection is one of the most important problems of modern data analysis. The sources of anomalies are varying. They can be the results of database users' mistakes, operational errors, or just missing values. The problem is very important because of the fast growth of large datasets. Therefore, in this article, we present detailed results of work on the concept of granular computing-based approach to anomaly detection, classification, and gradation. The aim of the study is to introduce an innovative solution that allows the use of information granules to identify and classify anomalies. The novelty of the proposed solution consists in the use of fuzzy semantics implied by the statistical properties of the data considered. Moreover, instead of the classic approach to detecting anomalies in the data, it is proposed to determine the degree of anomaly for the data transformed to the new resulting state space. Thanks to the use of an innovative approach using the universal descriptor space, it is possible to determine the degree of anomaly, and by using various aggregation methods one can also specify its type.

The introduction of domain knowledge opens new horizons to fuzzy clustering. Then knowledge-driven and data-driven fuzzy clustering methods come into being. To address the challenges of inadequate extraction mechanism and imperfect fusion mode in such class of methods, we propose the Knowledge-induced Multiple Kernel Fuzzy Clustering (KMKFC) algorithm. First, to extract knowledge points better, the Relative Density-based Knowledge Extraction (RDKE) method is proposed to extract high-density knowledge points close to cluster centers of real data structure, and provide initialized cluster centers. Moreover, the multiple kernel mechanism is introduced to improve the adaptability of clustering algorithm and map data to high-dimensional space, so as to better discover the differences between the data and obtain superior clustering results. Second, knowledge points generated by RDKE are integrated into KMKFC through a knowledge-influence matrix to guide the iterative process of KMKFC. Third, we also provide a strategy of automatically obtaining knowledge points, and thus propose the RDKE with Automatic knowledge acquisition (RDKE-A) method and the corresponding KMKFC-A algorithm. Then we prove the convergence of KMKFC and KMKFC-A. Finally, experimental studies demonstrate that the KMKFC and KMKFC-A algorithms perform better than thirteen comparison algorithms with regard to four evaluation indexes and the convergence speed.

This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation for multiplicative (ratio) pairwise comparisons has been provided. Counterexamples have been provided to support the theory. In our opinion, the scientific community must be made aware of the limitations of using the group theory in pairwise comparisons. Groups, which are not torsion free, cannot be used for ratios by Levi's theorems.