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The first edition of the Encyclopedia of Complexity and Systems Science (ECSS, 2009) presented a comprehensive overview of granular computing (GrC) broadly divided into several categories: Granular computing from rough set theory, Granular Computing in Database Theory, Granular Computing in Social Networks, Granular Computing and Fuzzy Set Theory, Grid/Cloud Computing, as well as general issues in granular computing. In 2011, the formal theory of GrC was established, providing an adequate infrastructure to support revolutionary new approaches to computer/data science, including the challenges presented by so-called big data. For this volume of ECSS, Second Edition, many entries have been updated to capture these new developments, together with new chapters on such topics as data clustering, outliers in data mining, qualitative fuzzy sets, and information flow analysis for security applications. Granulations can be seen as a natural and ancient methodology deeply rooted in the human mind. Many daily "things" are routinely granulated into sub "things": The topography of earth is granulated into hills, plateaus, etc., space and time are granulated into infinitesimal granules, and a circle is granulated into polygons of infinitesimal sides. Such granules led to the invention of calculus, topology and non-standard analysis. Formalization of general granulation was difficult but, as shown in this volume, great progress has been made in combing discrete and continuous mathematics under one roof for a broad range of applications in data science.

"Foundations of Data Mining and Knowledge Discovery" contains the latest results and new directions in data mining research. Data mining, which integrates various technologies, including computational intelligence, database and knowledge management, machine learning, soft computing, and statistics, is one of the fastest growing fields in computer science. Although many data mining techniques have been developed, further development of the field requires a close examination of its foundations. This volume presents the results of investigations into the foundations of the discipline, and represents the state of the art for much of the current research. This book will prove extremely valuable and fruitful for data mining researchers, no matter whether they would like to uncover the fundamental principles behind data mining, or apply the theories to practical applications.

Data-mining has become a popular research topic in recent years for the treatment of the "data rich and information poor" syndrome. Currently, application oriented engineers are only concerned with their immediate problems, which results in an ad hoc method of problem solving. Researchers, on the other hand, lack an understanding of the practical issues of data-mining for real-world problems and often concentrate on issues that are of no significance to the practitioners. In this volume, we hope to remedy problems by (1) presenting a theoretical foundation of data-mining, and (2) providing important new directions for data-mining research. A set of well respected data mining theoreticians were invited to present their views on the fundamental science of data mining. We have also called on researchers with practical data mining experiences to present new important data-mining topics.

The IEEE ICDM 2004 workshop on the Foundation of Data Mining and the IEEE ICDM 2005 workshop on the Foundation of Semantic Oriented Data and Web Mining focused on topics ranging from the foundations of data mining to new data mining paradigms. The workshops brought together both data mining researchers and practitioners to discuss these two topics while seeking solutions to long standing data mining problems and stimul- ing new data mining research directions. We feel that the papers presented at these workshops may encourage the study of data mining as a scienti?c ?eld and spark new communications and collaborations between researchers and practitioners. Toexpressthevisionsforgedintheworkshopstoawiderangeofdatam- ing researchers and practitioners and foster active participation in the study of foundations of data mining, we edited this volume by involving extended and updated versions of selected papers presented at those workshops as well as some other relevant contributions. The content of this book includes st- ies of foundations of data mining from theoretical, practical, algorithmical, and managerial perspectives. The following is a brief summary of the papers contained in this book.

Data-mining has become a popular research topic in recent years for the treatment of the "data rich and information poor" syndrome. Currently, application oriented engineers are only concerned with their immediate problems, which results in an ad hoc method of problem solving. Researchers, on the other hand, lack an understanding of the practical issues of data-mining for real-world problems and often concentrate on issues that are of no significance to the practitioners. In this volume, we hope to remedy problems by (1) presenting a theoretical foundation of data-mining, and (2) providing important new directions for data-mining research. A set of well respected data mining theoreticians were invited to present their views on the fundamental science of data mining. We have also called on researchers with practical data mining experiences to present new important data-mining topics.

The IEEE ICDM 2004 workshop on the Foundation of Data Mining and the IEEE ICDM 2005 workshop on the Foundation of Semantic Oriented Data and Web Mining focused on topics ranging from the foundations of data mining to new data mining paradigms. The workshops brought together both data mining researchers and practitioners to discuss these two topics while seeking solutions to long standing data mining problems and stimul- ing new data mining research directions. We feel that the papers presented at these workshops may encourage the study of data mining as a scienti?c ?eld and spark new communications and collaborations between researchers and practitioners. Toexpressthevisionsforgedintheworkshopstoawiderangeofdatam- ing researchers and practitioners and foster active participation in the study of foundations of data mining, we edited this volume by involving extended and updated versions of selected papers presented at those workshops as well as some other relevant contributions. The content of this book includes st- ies of foundations of data mining from theoretical, practical, algorithmical, and managerial perspectives. The following is a brief summary of the papers contained in this book.