Random Sets and Random Fuzzy Sets as Ill-Perceived Random Variables


Book Description

This short book provides a unified view of the history and theory of random sets and fuzzy random variables, with special emphasis on its use for representing higher-order non-statistical uncertainty about statistical experiments. The authors lay bare the existence of two streams of works using the same mathematical ground, but differing form their use of sets, according to whether they represent objects of interest naturally taking the form of sets, or imprecise knowledge about such objects. Random (fuzzy) sets can be used in many fields ranging from mathematical morphology, economics, artificial intelligence, information processing and statistics per se, especially in areas where the outcomes of random experiments cannot be observed with full precision. This book also emphasizes the link between random sets and fuzzy sets with some techniques related to the theory of imprecise probabilities. This small book is intended for graduate and doctoral students in mathematics or engineering, but also provides an introduction for other researchers interested in this area. It is written from a theoretical perspective. However, rather than offering a comprehensive formal view of random (fuzzy) sets in this context, it aims to provide a discussion of the meaning of the proposed formal constructions based on many concrete examples and exercises. This book should enable the reader to understand the usefulness of representing and reasoning with incomplete information in statistical tasks. Each chapter ends with a list of exercises.




Readings in Fuzzy Sets for Intelligent Systems


Book Description

Readings in Fuzzy Sets for Intelligent Systems is a collection of readings that explore the main facets of fuzzy sets and possibility theory and their use in intelligent systems. Basic notions in fuzzy set theory are discussed, along with fuzzy control and approximate reasoning. Uncertainty and informativeness, information processing, and membership, cognition, neural networks, and learning are also considered. Comprised of eight chapters, this book begins with a historical background on fuzzy sets and possibility theory, citing some forerunners who discussed ideas or formal definitions very close to the basic notions introduced by Lotfi Zadeh (1978). The reader is then introduced to fundamental concepts in fuzzy set theory, including symmetric summation and the setting of fuzzy logic; uncertainty and informativeness; and fuzzy control. Subsequent chapters deal with approximate reasoning; information processing; decision and management sciences; and membership, cognition, neural networks, and learning. Numerical methods for fuzzy clustering are described, and adaptive inference in fuzzy knowledge networks is analyzed. This monograph will be of interest to both students and practitioners in the fields of computer science, information science, applied mathematics, and artificial intelligence.




Fuzzy Sets and Their Applications to Cognitive and Decision Processes


Book Description

Fuzzy Sets and Their Applications to Cognitive and Decision Processes contains the proceedings of the U.S.-Japan Seminar on Fuzzy Sets and Their Applications, held at the University of California in Berkeley, California, on July 1-4, 1974. The seminar provided a forum for discussing a broad spectrum of topics related to the theory of fuzzy sets, ranging from its mathematical aspects to applications in human cognition, communication, decision making, and engineering systems analysis. Comprised of 19 chapters, this book begins with an introduction to the calculus of fuzzy restrictions, followed by a discussion on fuzzy programs and their execution. Subsequent chapters focus on fuzzy relations, fuzzy graphs, and their applications to clustering analysis; risk and decision making in a fuzzy environment; fractionally fuzzy grammars and their application to pattern recognition; and applications of fuzzy sets in psychology. An approach to pattern recognition and associative memories using fuzzy logic is also described. This monograph will be of interest to students and practitioners in the fields of computer science, engineering, psychology, and applied mathematics.




Handbook of Bayesian, Fiducial, and Frequentist Inference


Book Description

The emergence of data science, in recent decades, has magnified the need for efficient methodology for analyzing data and highlighted the importance of statistical inference. Despite the tremendous progress that has been made, statistical science is still a young discipline and continues to have several different and competing paths in its approaches and its foundations. While the emergence of competing approaches is a natural progression of any scientific discipline, differences in the foundations of statistical inference can sometimes lead to different interpretations and conclusions from the same dataset. The increased interest in the foundations of statistical inference has led to many publications, and recent vibrant research activities in statistics, applied mathematics, philosophy and other fields of science reflect the importance of this development. The BFF approaches not only bridge foundations and scientific learning, but also facilitate objective and replicable scientific research, and provide scalable computing methodologies for the analysis of big data. Most of the published work typically focusses on a single topic or theme, and the body of work is scattered in different journals. This handbook provides a comprehensive introduction and broad overview of the key developments in the BFF schools of inference. It is intended for researchers and students who wish for an overview of foundations of inference from the BFF perspective and provides a general reference for BFF inference. Key Features: Provides a comprehensive introduction to the key developments in the BFF schools of inference Gives an overview of modern inferential methods, allowing scientists in other fields to expand their knowledge Is accessible for readers with different perspectives and backgrounds




Relational Calculus for Actionable Knowledge


Book Description

This book focuses on one of the major challenges of the newly created scientific domain known as data science: turning data into actionable knowledge in order to exploit increasing data volumes and deal with their inherent complexity. Actionable knowledge has been qualitatively and intensively studied in management, business, and the social sciences but in computer science and engineering, its connection has only recently been established to data mining and its evolution, ‘Knowledge Discovery and Data Mining’ (KDD). Data mining seeks to extract interesting patterns from data, but, until now, the patterns discovered from data have not always been ‘actionable’ for decision-makers in Socio-Technical Organizations (STO). With the evolution of the Internet and connectivity, STOs have evolved into Cyber-Physical and Social Systems (CPSS) that are known to describe our world today. In such complex and dynamic environments, the conventional KDD process is insufficient, and additional processes are required to transform complex data into actionable knowledge. Readers are presented with advanced knowledge concepts and the analytics and information fusion (AIF) processes aimed at delivering actionable knowledge. The authors provide an understanding of the concept of ‘relation’ and its exploitation, relational calculus, as well as the formalization of specific dimensions of knowledge that achieve a semantic growth along the AIF processes. This book serves as an important technical presentation of relational calculus and its application to processing chains in order to generate actionable knowledge. It is ideal for graduate students, researchers, or industry professionals interested in decision science and knowledge engineering.




Classic Works of the Dempster-Shafer Theory of Belief Functions


Book Description

This is a collection of classic research papers on the Dempster-Shafer theory of belief functions. The book is the authoritative reference in the field of evidential reasoning and an important archival reference in a wide range of areas including uncertainty reasoning in artificial intelligence and decision making in economics, engineering, and management. The book includes a foreword reflecting the development of the theory in the last forty years.




Computer Aided Systems Theory - CAST '94


Book Description

This volume presents a collection of revised refereed papers selected from the presentations at the Fourth International Workshop on Computer Aided Systems Theory - CAST '94, held in Ottawa, Ontario, Canada in May 1994. The 31 full papers included in the book were chosen from originally 82 submissions and reflect the state of the art in the area of computer aided systems theory. The volume is divided into sections on foundations, methods, and tools and environments.







Engineering Design Reliability Handbook


Book Description

Researchers in the engineering industry and academia are making important advances on reliability-based design and modeling of uncertainty when data is limited. Non deterministic approaches have enabled industries to save billions by reducing design and warranty costs and by improving quality. Considering the lack of comprehensive and defini




Symbolic and Quantitative Approaches to Reasoning with Uncertainty


Book Description

These are the proceedings of the 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2005, held in Barcelona (Spain), July 6–8, 2005. The ECSQARU conferences are biennial and have become a major forum for advances in the theory and practice of r- soning under uncertainty. The ?rst ECSQARU conference was held in Marseille (1991), and after in Granada (1993), Fribourg (1995), Bonn (1997), London (1999), Toulouse (2001) and Aalborg (2003). The papers gathered in this volume were selected out of 130 submissions, after a strict review process by the members of the Program Committee, to be presented at ECSQARU 2005. In addition, the conference included invited lectures by three outstanding researchers in the area, Seraf ́ ?n Moral (Imprecise Probabilities), Rudolf Kruse (Graphical Models in Planning) and J ́ erˆ ome Lang (Social Choice). Moreover, the application of uncertainty models to real-world problems was addressed at ECSQARU 2005 by a special session devoted to s- cessful industrial applications, organized by Rudolf Kruse. Both invited lectures and papers of the special session contribute to this volume. On the whole, the programme of the conference provided a broad, rich and up-to-date perspective of the current high-level research in the area which is re?ected in the contents of this volume. IwouldliketowarmlythankthemembersoftheProgramCommitteeandthe additional referees for their valuable work, the invited speakers and the invited session organizer.