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The Theory of Cluster Sets
An introduction to the theory of cluster sets, a branch of topological analysis.
Cluster Sets
For the first systematic investigations of the theory of cluster sets of analytic functions, we are indebted to IVERSEN [1-3J and GROSS [1-3J about forty years ago. Subsequent important contributions before 1940 were made by SEIDEL [1-2J, DOOE [1-4J, CARTWRIGHT [1-3J and BEURLING [1]. The investigations of SEIDEL and BEURLING gave great impetus and interest to Japanese mathematicians; beginning about 1940 some contributions were made to the theory by KUNUGUI [1-3J, IRIE [IJ, TOKI [IJ, TUMURA [1-2J, KAMETANI [1-4J, TsuJI [4J and NOSHIRO [1-4J. Recently, many noteworthy advances have been made by BAGEMIHL, SEIDEL, COLLINGWOOD, CARTWRIGHT, HERVE, LEHTO, LOHWATER, MEIER, OHTSUKA and many other m...
A Journey into Ambiguous Set Theory
The book provides a comprehensive introduction to ambiguous set theory, offering readers a clear understanding of the fundamental concepts and principles underlying this intriguing branch of mathematics. It explores the historical development of ambiguous set theory, tracing its roots and evolution over time. Readers are introduced to the foundational principles of ambiguous set theory, including its axioms, definitions, and basic theorems. Through concrete examples and case studies, the book demonstrates the practical applications of ambiguous set theory across various disciplines, and applications of ambiguous set theory in decision-making, control systems, and medical imaging. It is designed to be approachable for readers with varying levels of mathematical background, making it suitable for students, researchers, and enthusiasts alike.
Fuzzy Set Theory—and Its Applications
Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.
Applications of Fuzzy Sets Theory
The 7th International Workshop on Fuzzy Logic and Applications, held in Camogli, Italy in July 2007, presented the latest findings in the field. This volume features the refereed proceedings from that meeting. It includes 84 full papers as well as three keynote speeches. The papers are organized into topical sections covering fuzzy set theory, fuzzy information access and retrieval, fuzzy machine learning, and fuzzy architectures and systems.
Fuzzy Sets in Information Retrieval and Cluster Analysis
The present monograph intends to establish a solid link among three fields: fuzzy set theory, information retrieval, and cluster analysis. Fuzzy set theory supplies new concepts and methods for the other two fields, and provides a common frame work within which they can be reorganized. Four principal groups of readers are assumed: researchers or students who are interested in (a) application of fuzzy sets, (b) theory of information retrieval or bibliographic databases, (c) hierarchical clustering, and (d) application of methods in systems science. Readers in group (a) may notice that the fuzzy set theory used here is very simple, since only finite sets are dealt with. This simplification ena...
Rough Set Theory: A True Landmark in Data Analysis
Part 1 of this book deals with theoretical contributions of rough set theory, and parts 2 and 3 focus on several real world data mining applications. The book thoroughly explores recent results in rough set research.
Handbook of Research on Fuzzy and Rough Set Theory in Organizational Decision Making
Soft computing techniques are innovative tools that use nature-inspired algorithms to run predictive analysis of industries from business to software measurement. These tools have gained momentum in recent years for their practicality and flexibility. The Handbook of Research on Fuzzy and Rough Set Theory in Organizational Decision Making collects both empirical and applied research in the field of fuzzy set theory, and bridges the gap between the application of soft computational approaches and the organizational decision making process. This publication is a pivotal reference for business professionals, IT specialists, software engineers, and advanced students of business and information technology.
Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review
Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory.
