Information granules are fundamental conceptual entities facilitating perception of complex phenomena and contributing to the enhancement of human centricity in intelligent systems. The formal frameworks of information granules and information granulation comprise fuzzy sets, interval analysis, probability, rough sets, and shadowed sets, to name only a few representatives. Among current developments of Granular Computing, interesting options concern information granules of higher order and of higher type. The higher order information granularity is concerned with an effective formation of information granules over the space being originally constructed by information granules of lower order. This construct is directly associated with the concept of hierarchy of systems composed of successive processing layers characterized by the increasing levels of abstraction. This idea of layered, hierarchical realization of models of complex systems has gained a significant level of visibility in fuzzy modeling with the well-established concept of hierarchical fuzzy models where one strives to achieve a sound tradeoff between accuracy and a level of detail captured by the model and its level of interpretability. Higher type information granules emerge when the information granules themselves cannot be fully characterized in a purely numerical fashion but instead it becomes convenient to exploit their realization in the form of other types of information granules such as type-2 fuzzy sets, interval-valued fuzzy sets, or probabilistic fuzzy sets. Higher order and higher type of information granules constitute the focus of the studies on Granular Computing presented in this study. The book elaborates on sound methodologies of Granular Computing, algorithmic pursuits and an array of diverse applications and case studies in environmental studies, option price forecasting, and power engineering.

Information granules, as encountered in natural language, are implicit in nature. To make them fully operational so they can be effectively used to analyze and design intelligent systems, information granules need to be made explicit. An emerging discipline, granular computing focuses on formalizing information granules and unifying them to create a coherent methodological and developmental environment for intelligent system design and analysis. Granular Computing: Analysis and Design of Intelligent Systems presents the unified principles of granular computing along with its comprehensive algorithmic framework and design practices. Introduces the concepts of information granules, information granularity, and granular computing Presents the key formalisms of information granules Builds on the concepts of information granules with discussion of higher-order and higher-type information granules Discusses the operational concept of information granulation and degranulation by highlighting the essence of this tandem and its quantification in terms of the associated reconstruction error Examines the principle of justifiable granularity Stresses the need to look at information granularity as an important design asset that helps construct more realistic models of real-world systems or facilitate collaborative pursuits of system modeling Highlights the concepts, architectures, and design algorithms of granular models Explores application domains where granular computing and granular models play a visible role, including pattern recognition, time series, and decision making Written by an internationally renowned authority in the field, this innovative book introduces readers to granular computing as a new paradigm for the analysis and synthesis of intelligent systems. It is a valuable resource for those engaged in research and practical developments in computer, electrical, industrial, manufacturing, and biomedical engineering. Building from fundamentals, the book is also suitable for readers from nontechnical disciplines where information granules assume a visible position.

This book offers a comprehensive treatise on the recent pursuits of Artificial Intelligence (AI) – Explainable Artificial Intelligence (XAI) by casting the crucial features of interpretability and explainability in the original framework of Granular Computing. The innovative perspective established with the aid of information granules provides a high level of human centricity and transparency central to the development of AI constructs. The chapters reflect the breadth of the area and cover recent developments in the methodology, advanced algorithms and applications of XAI to visual analytics, knowledge representation, learning and interpretation. The book appeals to a broad audience including researchers and practitioners interested in gaining exposure to the rapidly growing body of knowledge in AI and intelligent systems.

Granular Computing is concerned with constructing and processing carried out at the level of information granules. Using information granules, we comprehend the world and interact with it, no matter which intelligent endeavor this may involve. The landscape of granular computing is immensely rich and involves set theory (interval mathematics), fuzzy sets, rough sets, random sets linked together in a highly synergetic environment. This volume is a first comprehensive treatment of this emerging paradigm and embraces its fundamentals, underlying methodological framework, and a sound algorithmic environment. The panoply of applications covered includes system identification, telecommunications, linguistics and music processing. Written by experts in the field, this volume will appeal to all developing intelligent systems, either working at the methodological level or interested in detailed system realization.

This book explores the significant role of granular computing in advancing machine learning towards in-depth processing of big data. It begins by introducing the main characteristics of big data, i.e., the five Vs—Volume, Velocity, Variety, Veracity and Variability. The book explores granular computing as a response to the fact that learning tasks have become increasingly more complex due to the vast and rapid increase in the size of data, and that traditional machine learning has proven too shallow to adequately deal with big data. Some popular types of traditional machine learning are presented in terms of their key features and limitations in the context of big data. Further, the book discusses why granular-computing-based machine learning is called for, and demonstrates how granular computing concepts can be used in different ways to advance machine learning for big data processing. Several case studies involving big data are presented by using biomedical data and sentiment data, in order to show the advances in big data processing through the shift from traditional machine learning to granular-computing-based machine learning. Finally, the book stresses the theoretical significance, practical importance, methodological impact and philosophical aspects of granular-computing-based machine learning, and suggests several further directions for advancing machine learning to fit the needs of modern industries. This book is aimed at PhD students, postdoctoral researchers and academics who are actively involved in fundamental research on machine learning or applied research on data mining and knowledge discovery, sentiment analysis, pattern recognition, image processing, computer vision and big data analytics. It will also benefit a broader audience of researchers and practitioners who are actively engaged in the research and development of intelligent systems.

Information granules, as encountered in natural language, are implicit in nature. To make them fully operational so they can be effectively used to analyze and design intelligent systems, information granules need to be made explicit. An emerging discipline, granular computing focuses on formalizing information granules and unifying them to create a coherent methodological and developmental environment for intelligent system design and analysis. Granular Computing: Analysis and Design of Intelligent Systems presents the unified principles of granular computing along with its comprehensive algorithmic framework and design practices. Introduces the concepts of information granules, information granularity, and granular computing Presents the key formalisms of information granules Builds on the concepts of information granules with discussion of higher-order and higher-type information granules Discusses the operational concept of information granulation and degranulation by highlighting the essence of this tandem and its quantification in terms of the associated reconstruction error Examines the principle of justifiable granularity Stresses the need to look at information granularity as an important design asset that helps construct more realistic models of real-world systems or facilitate collaborative pursuits of system modeling Highlights the concepts, architectures, and design algorithms of granular models Explores application domains where granular computing and granular models play a visible role, including pattern recognition, time series, and decision making Written by an internationally renowned authority in the field, this innovative book introduces readers to granular computing as a new paradigm for the analysis and synthesis of intelligent systems. It is a valuable resource for those engaged in research and practical developments in computer, electrical, industrial, manufacturing, and biomedical engineering. Building from fundamentals, the book is also suitable for readers from nontechnical disciplines where information granules assume a visible position.