In the evolving framework of granular computing, the continuous flow of data, often referred to as data streaming, presents both challenges and opportunities for the granulation process. Building upon the foundational works of Professor Zadeh and the granulation techniques based in rough set theory, this paper investigates the integration of data streaming with the concept-dependent granulation method. Recognizing the inherent challenges posed by the vastness and dynamism of streaming data, we explore the potential of adapting the concept-dependent granulation to accommodate and process these streams efficiently. Drawing inspiration from our previous works on random sampling and data decomposition, we introduce a novel approach that utilizes the real-time nature of data streams to enhance the granulation process. Our experimental studies, aim to evaluate the effectiveness of this method in terms of granulation quality and computational efficiency. Preliminary results suggest that integrating data streaming with concept-dependent granulation not only preserves the integrity of the granulated information but also offers significant advantages in processing large-scale dynamic data. In this work, we have verified the possibility of detecting the amount of data necessary to achieve the relevant classification efficiency, without having to process the entire data. This paper serves as a bridge, connecting the established methodologies of granulation with the emerging challenges of big data streaming, and sets the foundation for future research in this domain.

The granular computing approach as a paradigm in approximate reasoning deals with the processing of knowledge into granules that consist of entities similar in information content. Within the framework of rough set theory, proposed 40 years ago by Zdzislaw Pawlak and developed since then by many authors, granulation is an important area of research. Granulation techniques have found application in many areas of data mining in classification, feature selection, clustering and approximation processes for decision-making systems, among others. The current work is located in the development of approximation techniques for decision systems using rough inclusions proposed by Polkowski. Polkowski proposed the hypothesis that granules induced in a data set of a universe of objects should lead to new object representing them, and such granulated counterparts should preserve the information content of the data. This hypothesis has been verified in a number of research papers by Polkowski and Artiemjew. It has been proven that one of the best granulation techniques from the proposed family of methods is concept-dependent granulation. In which, on selected data, the degree of approximation of decision-making systems reaches more than 90 percent reduction in the size of training systems while maintaining the classification efficiency of the original training data. The undoubted disadvantage of this technique is the quadratic computational complexity - which forces us to look for a way to apply it on big data sets.The current work is one in a series of papers on the application of techniques used to deal with big data sets in the context of accelerating the concept-dependent granulation method. In this paper, we test whether granulation of training data divided into subgroups with post-granulation object fusion is competitive - in terms of running time and classification efficiency - to using a full training system in the granulation and classification process. The posed experimental problem is verified on a selected decision-making systems from UCI repository and using simple kNN classifier.

This work extends the authors' contribution to the International Conference on Rough Sets and Current Trends in Computing (RSCTC 2008) held at the University of Akron in October 2008. It is dedicated to the topic of granular computing, formalized within the theory of rough mereology, as proposed by Polkowski; as an application of the idea of a granular reflection of data and of classifiers induced from it (Polkowski, 2005), we give an account of recent results in this area. A scheme for classifier construction based on factoring a classifier through a granular reflection of data; voting by granules of training objects; voting by granules of decision rules induced from the training set; voting by granules induced from a granular reflection of data, is presented here. In voting cases, voting is based on weights computed by means of rough inclusions induced from residual implications of continuous t-norms. The results show a high effectiveness of this approach as witnessed by the reported tests with some well--known data sets from University of California, at Irvine (UCI) repository whose results are compared against the standard rough set exhaustive classifier whose accuracy is indicated under the radius of “nil.” © 2011 Wiley Periodicals, Inc.