This book constitutes the refereed post-conference proceedings of the 4th International Conference on Intelligence Science, ICIS 2020, held in Durgapur, India, in February 2021 (originally November 2020). The 23 full papers and 4 short papers presented were carefully reviewed and selected from 42 submissions. One extended abstract is also included. They deal with key issues in brain cognition; uncertain theory; machine learning; data intelligence; language cognition; vision cognition; perceptual intelligence; intelligent robot; and medical artificial intelligence.

'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.

Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields.

'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets.

This book constitutes the refereed post-conference proceedings of the 4th International Conference on Intelligence Science, ICIS 2020, held in Durgapur, India, in February 2021 (originally November 2020). The 23 full papers and 4 short papers presented were carefully reviewed and selected from 42 submissions. One extended abstract is also included. They deal with key issues in brain cognition; uncertain theory; machine learning; data intelligence; language cognition; vision cognition; perceptual intelligence; intelligent robot; and medical artificial intelligence.

'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost.

Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields.

'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets.

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."

This book constitutes the refereed proceedings of the 12th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2009, held in Delhi, India in December 2009 in conjunction with the Third International Conference on Pattern Recognition and Machine Intelligence, PReMI 2009. RSFDGrC 2009 is the core component of a broader Rough Set Year in India initiative, RSIndia09.

The 56 revised full papers presented together with 6 invited papers and a report on the Rough Set Year in India 2009 project were carefully reviewed and selected from a total of 130 submissions. The papers are organized in topical sections on foundations of rough sets and beyond; rought set algorithms and applications; fuzzy set foundations and applications; data mining and knowledge discovery; clustering and current trends in computing; and information retrieval and text mining.