Rough Set Theory: Ontological Systems, Entailment Relations and Approximation Operators -- Information Entropy and Granulation Co–Entropy of Partitions and Coverings: A Summary -- Lattices with Interior and Closure Operators and Abstract Approximation Spaces -- Rough Approximation Based on Weak q-RIFs -- Rough Geometry and Its Applications in Character Recognition -- Extensions of Information Systems: The Rough Set Perspective -- Intangible Assets in a Polish Telecommunication Sector – Rough Sets Approach -- Multicriteria Attractiveness Evaluation of Decision and Association Rules.

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 tenth volume of the Transactions on Rough Sets series, provides evidence of further growth in the rough set landscape, both in terms of its foundations and its applications. The 8 papers presented in this volume focus on a number of research streams that were either directly or indirectly begun by the seminal work on rough sets by Zdzislaw Pawlak for a number of research areas such as entailment and approximation operators, extensions of information systems, information entropy and granulation, lattices, multicriteria attractiveness evaluation of decision and association rules, ontological systems, rough approximation, and rough geometry in image analysis.