Volume IV of the Transactions on Rough Sets (TRS) introduces a number of new advances in the theory and application of rough sets. Rough sets and - proximationspaceswereintroducedmorethan30yearsagobyZdzis lawPawlak. These advances have profound implications in a number of research areas such as the foundations of rough sets, approximate reasoning, arti?cial intelligence, bioinformatics,computationalintelligence, cognitivescience, intelligentsystems, datamining,machineintelligence,andsecurity. Inaddition,itisevidentfromthe papers included in this volume that the foundations and applications of rough sets is a very active research area worldwide. A total of 16 researchers from 7 countries are represented in this volume, namely, Canada, India, Norway, S- den, Poland, Russia and the United States of America. Evidence of the vigor, breadth and depth of research in the theory and applications of rough sets can be found in the 10 articles in this volume. Prof. Pawlak has contributed a treatise on the philosophical underpinnings of rough sets. In this treatise, observations are made about the Cantor notion of a set, antinomies arising from Cantor sets, the problem of vagueness (es- cially, vague (imprecise) concepts), fuzzy sets, rough sets, fuzzy vs. rough sets as well as logic and rough sets. Among the many vistas and research directions suggested by Prof. Pawlak, one of the most fruitful concerns the model for a rough membership function, which was incarnated in many di?erent forms since its introduction by Pawlakand Skowronin 1994. Recall, here, that Prof.

This book, which constitutes the tenth volume of the Transactions on Rough Sets series, focuses on a number of research streams that were either directly or indirectly begun by the seminal work on rough sets by Zdzislaw Pawlak.

Annotation 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 VI of the Transactions on Rough Sets (TRS) commemorates the life and work of Zdzislaw Pawlak (1926-2006). His legacy is rich and varied. Prof. Pawlak's research contributions have had far-reaching implications inasmuch as his works are fundamental in establishing new perspectives for scientific research in a wide spectrum of fields. This volume of the TRS presents papers that reflect the profound influence of a number of research initiatives by Professor Pawlak. In particular, this volume introduces a number of new advances in the foundations and applications of artificial intelligence, engineering, logic, mathematics, and science. These advances have significant implications in a number of research areas such as the foundations of rough sets, approximate reasoning, bioinformatics, computational intelligence, cognitive science, data mining, information systems, intelligent systems, machine intelligence, and security.

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 XX 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.

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 XVII is a continuation of a number of research streams which have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the 21st century. The research streams represented in the papers cover both theory and applications of rough, fuzzy and near sets as well as their combinations.

Together with volume VI of the Transactions on Rough Sets series, this book commemorates the life and work of Zdzislaw Pawlak (1926-2006). It presents papers that reflect the profound influence of a number of research initiatives by Professor Pawlak, introducing a number of advances in the foundations and applications of AI, engineering, logic, mathematics, and science, which have had significant implications in a number of research areas.

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 XXI 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.

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.

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. This book, which constitutes the eighth volume of the Transactions on Rough Sets series, contains a wide spectrum of contributions to the theory and applications of rough sets. The 17 papers presented explore several research streams and introduce a number of new advances in the foundations and applications of artificial intelligence, engineering, logic, mathematics, and science.

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.