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Elements of the Representation Theory of Associative Algebras: Volume 1
This is the first of a two-volume set that provides a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. The treatment is self-contained and provides an elementary and up-to-date introduction to the subject using quiver-theoretical techniques and the theory of almost split sequences as well as tilting theory and the use of integral quadratic forms. Much of this material has never appeared before in book form. The book is primarily addressed to graduate students starting research in the representation theory of algebras, but it will also be of interest to mathematicians in other fields. The text includes many illustrative examples and a large number of exercises at the end of each of the ten chapters. Proofs are presented in complete detail, making the book suitable for courses, seminars, and self-study. Book jacket.
Transactions on Rough Sets V
This book is dedicated to the monumental life, work and creative genius of Zdzislaw Pawlak, the originator of rough sets, who passed away in April 2006. It opens with a commemorative article that gives a brief coverage of Pawlak's works in rough set theory, molecular computing, philosophy, painting and poetry. Fifteen papers explore the theory of rough sets in various domains as well as new applications of rough sets.
Rough-Neural Computing
Soft computing comprises various paradigms dedicated to approximately solving real-world problems, e.g. in decision making, classification or learning; among these paradigms are fuzzy sets, rough sets, neural networks, genetic algorithms, and others. It is well understood now in the soft computing community that hybrid approaches combining various paradigms are very promising approaches for solving complex problems. Exploiting the potential and strength of both neural networks and rough sets, this book is devoted to rough-neuro computing which is also related to the novel aspect of computing based on information granulation, in particular to computing with words. It provides foundational and methodological issues as well as applications in various fields.
Transactions on Rough Sets XXIII
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. Volume XXIII in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.
New Directions in Rough Sets, Data Mining, and Granular-Soft Computing
This book constitutes the refereed proceedings of the 7th International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, RSFDGrC'99, held in Yamaguchi, Japan, in November 1999. The 45 revised regular papers and 15 revised short papers presented together with four invited contributions were carefully reviewed and selected from 89 submissions. The book is divided into sections on rough computing: foundations and applications, rough set theory and applications, fuzzy set theory and applications, nonclassical logic and approximate reasoning, information granulation and granular computing, data mining and knowledge discovery, machine learning, and intelligent agents and systems.
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Handbook of Granular Computing
Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years have witnessed a renewed and expanding interest in the topic as it begins to play a key role in bioinformatics, e-commerce, machine learning, security, data mining and wireless mobile computing when it comes to the issues of effectiveness, robustness and uncertainty. The Handbook of Granular Computing offers a comprehensive reference source for the granular computing community, edited by and with...
Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam
This book is dedicated to the memory of Professor Zdzis{\l}aw Pawlak who passed away almost six year ago. He is the founder of the Polish school of Artificial Intelligence and one of the pioneers in Computer Engineering and Computer Science with worldwide influence. He was a truly great scientist, researcher, teacher and a human being. This book prepared in two volumes contains more than 50 chapters. This demonstrates that the scientific approaches discovered by of Professor Zdzis{\l}aw Pawlak, especially the rough set approach as a tool for dealing with imperfect knowledge, are vivid and intensively explored by many researchers in many places throughout the world. The submitted papers prove that interest in rough set research is growing and is possible to see many new excellent results both on theoretical foundations and applications of rough sets alone or in combination with other approaches. We are proud to offer the readers this book.
Transactions on Rough Sets I
The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, starting from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence. This first volume of the Transactions on Rough Sets opens with an introductory article by Zdzislaw Pawlak, the originator of rough sets. Nine papers deal with rough set theory and eight are devoted to applications in various domains.
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