James F. Peters

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 XVI includes extensions of papers from the Rough Sets and Knowledge Technology Conference which was held in Banff, Canada, in October 2011. In addition this book contains a long paper based on a PhD thesis. The papers cover both theory and applications of rough, fuzzy and near sets. They offer 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 principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces. This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising. It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications -- P. of cover.

We would like to present, with great pleasure, the ?rst volume of a new jo- nal, Transactions on Rough Sets. This journal, part of the new journal subline in the Springer-Verlag series Lecture Notes in Computer Science, is devoted to the entire spectrum of rough set related issues, starting from logical and ma- ematical foundations of rough sets, through all aspects of rough set theory and its applications, 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, theory of evidence, etc. The ?rst, pioneering papers on rough sets, written by the originator of the idea,ProfessorZdzis lawPawlak,werepublishedintheearly1980s.Weareproud to dedicate this volume to our mentor, Professor Zdzis law Pawlak, who kindly enriched this volume with his contribution on philosophical, logical, and mat- matical foundations of roughset theory. In his paper Professor Pawlakshows all over again the underlying ideas of rough set theory as well as its relations with Bayes’ theorem, con?ict analysis, ?ow graphs, decision networks, and decision rules.