Transactions on Rough Sets X: Vol 5656

Volume X of the Transactions on Rough Sets (TRS) provides evidence of further growth in the rough set landscape, both in terms of its foundations and its applications. This volume of the TRS re?ects a number of research streams that were eitherdirectly orindirectly begunbytheseminalworkonroughsetsbyZdzis law 1 Pawlak (1926-2006) . This seminal work started with Zdzis law Pawlak's early 1970s work on knowledge description systems prior to his discovery of rough sets during the early 1980s. Evidence of the growth of various rough set-based 2 research streams can be found in the rough set database . This volume includes articles that are part of a special issue on "Foundations ofRoughSets"originallyproposedbyMihirChakraborty.Inadditiontoresearch on the foundations of rough sets, this volume of the TRS also presents papers that re?ect the profound in?uence of a number of other research initiatives by Zdzis law Pawlak. In particular, this volume introduces a number of new advances in the fo- dations of rough sets. These advances have signi?cant implications in a number of research areas such as entailment and approximation operators, extensions of informationsystems, informationentropyand granulation, lattices, multicriteria attractiveness evaluation of decision and association rules, ontological systems, rough approximation, and rough geometry in image analysis. ThisvolumeoftheTRShasbeenmadepossiblethankstothelaudablee?orts ofagreatmanygenerouspersonsandorganizations.Weextendourthankstothe following reviewers: Cheng Ching-Hsue, MartineDeCock, IvoDun ] tsch, Jianwen Fang, Anna Gomolin ´ska, Salvatore Greco, Jerzy W. Grzyma la-Busse, Masahiro Inuiguchi, Szymon Jaroszewicz, Jouni Ja ]rvinen, Piero Pagliani, Sankar Kumar Pal, Lech Polkowski, Yuhua Qian, Jaros law Stepaniuk, Wojciech Ziarko and Yiyu Yao.

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.