Quotient Space Based Problem Solving

Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search. Explains the theory of hierarchical problem solving, its computational complexity, and discusses the principle and applications of multi-granular computing Describes a human-like, theoretical framework using quotient space theory, that will be of interest to researchers in artificial intelligence Provides many applications and examples in the engineering and computer science area Includes complete coverage of planning, heuristic search and coverage of strictly mathematical models

This book constitutes the refereed proceedings of the First International Conference on Rough Sets and Knowledge Technology, RSKT 2006, held in Chongqing, China in July 2006. The volume presents 43 revised full papers and 58 revised short papers, together with 15 commemorative and invited papers. Topics include rough computing, evolutionary computing, fuzzy sets, granular computing, neural computing, machine learning and KDD, logics and reasoning, multiagent systems and Web intelligence, and more.

This book presents the fundamental and technical concepts of fuzzy hypergraphs and explains their extensions and applications. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, m-polar fuzzy, Pythagorean, complex Pythagorean, and q-rung orthopair hypergraphs, as well as single-valued neutrosophic, complex neutrosophic and bipolar neutrosophic hypergraphs. In addition, the book also sheds light on real-world applications of these hypergraphs, making it a valuable resource for students and researchers in the field of mathematics, as well as computer and social scientists.

The recent pursuits emerging in the realm of big data processing, interpretation, collection and organization have emerged in numerous sectors including business, industry and government organizations. Data sets such as customer transactions for a mega-retailer, weather monitoring, intelligence gathering, quickly outpace the capacities of traditional techniques and tools of data analysis. The 3V (volume, variability and velocity) challenges led to the emergence of new techniques and tools in data visualization, acquisition, and serialization. Soft Computing being regarded as a plethora of technologies of fuzzy sets (or Granular Computing), neurocomputing and evolutionary optimization brings forward a number of unique features that might be instrumental to the development of concepts and algorithms to deal with big data. This carefully edited volume provides the reader with an updated, in-depth material on the emerging principles, conceptual underpinnings, algorithms and practice of Computational Intelligence in the realization of concepts and implementation of big data architectures, analysis, and interpretation as well as data analytics. The book is aimed at a broad audience of researchers and practitioners including those active in various disciplines in which big data, their analysis and optimization are of genuine relevance. One focal point is the systematic exposure of the concepts, design methodology, and detailed algorithms. In general, the volume adheres to the top-down strategy starting with the concepts and motivation and then proceeding with the detailed design that materializes in specific algorithms and representative applications. The material is self-contained and provides the reader with all necessary prerequisites and augments some parts with a step-by-step explanation of more advanced concepts supported by a significant amount of illustrative numeric material and some application scenarios to motivate the reader and make some abstract concepts more tangible.

This book constitutes the refereed proceedings of the 5th International Conference on Rough Set and Knowledge Technology, RSKT 2010, held in Beijing, China, in October 2010. The 98 revised full papers papers presented were carefully reviewed and selected from 175 initial submissions. The papers are organized in topical sections on rough sets and computing theory, fuzzy sets, knowledge technology, intelligent information processing, health informatics and biometrics authentication, neural networks, complex networks, granular computing, metaheuristic, cloud model and its application, data mining in cloud computing, decision-theoretic rough set model, and quotient space theory research and application.

Research results obtained by the authors in recent years form the basis of this volume. The motivation behind this research is the authors' belief that more human-like characteristics in problem solving should be involved in a formal representation in order to achieve better performance for computer-based problem solvers. A large part of the material is presented in the language of mathematics, including elementary topology, set theory and statistics. To help the less mathematically-trained readers follow the basic concepts and techniques, basic definitions and theorems are presented before the discussions. A conscious effort is made to introduce simple examples and applications in each topic. This book is designed for graduate students, research fellows and technicians in Computer Science, especially Artificial Intelligence, and also those concerned with computerised problem solving.

This book contains selected chapters on recent research in topology. It bridges the gap between recent trends of topological theories and their applications in areas like social sciences, natural sciences, soft computing, economics, theoretical chemistry, cryptography, pattern recognitions and granular computing. There are 14 chapters, including two chapters on mathematical economics from the perspective of topology. The book discusses topics on function spaces, relator space, preorder, quasi-uniformities, bitopological dynamical systems, b-metric spaces and related fixed point theory. This book is useful to researchers, experts and scientists in studying the cutting-edge research in topology and related areas and helps them applying topology in solving real-life problems the society and science are facing these days.