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 ninth volume of the Transactions on Rough Sets series, providing evidence of the continuing growth of a number of research streams. It includes articles that are extensions of papers included in the first conference on Rough Sets and Intelligent Systems Paradigms. The 26 papers presented in this volume introduce a number of new advances in the foundations and applications of artificial intelligence, engineering, image processing, logic, mathematics, medicine, music, 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.

This two-volume set LNAI 10313 and LNAI 10314 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2017, held in Olsztyn, Poland, in July 2017. The 74 revised full papers presented together with 16 short papers and 16 invited talks, were carefully reviewed and selected from 130 submissions. The papers in this two set-volume of IJCRS 2017 follow the track already rutted by RSCTC and JRS conferences which aimed at unification of many facets of rough set theory from theoretical aspects of the rough set idea bordering on theory of concepts and going through algebraic structures, topological structures, logics for uncertain reasoning, decision algorithms, relations to other theories of vagueness and ambiguity, then to extensions of the rough set idea like granular structures, rough mereology, and to applications of the idea in diverse fields of applied science including hybrid methods like rough-fuzzy, neuro-rough, neuro-rough-fuzzy computing. IJCRS 2017 encompasses topics spread among four main tracks: Rough Sets and Data Science (in relation to RSCTC series organized since 1998); Rough Sets and Granular Computing (in relation to RSFDGrC series organized since 1999); Rough Sets and Knowledge Technology (in relation to RSKT series organized since 2006); and Rough Sets and Intelligent Systems (in relation to RSEISP series organized since 2007).

This book constitutes the refereed proceedings of the 7th International Conference on Rough Sets and Current Trends in Computing, RSCTC 2010, held in Warsaw, Poland, in June 2010.

This book constitutes the refereed proceedings of the 13th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2011, held in Moscow, Russia in June 2011. The 49 revised full papers presented together with 5 invited and 2 tutorial papers were carefully reviewed and selected from a total of 83 submissions. The papers are organized in topical sections on rough sets and approximations, coverings and granules, fuzzy set models, fuzzy set applications, compound values, feature seletion and reduction, clusters and concepts, rules and trees, image processing, and interactions and visualization.

This book constitutes the refereed proceedings of the 6th International Conference on Rough Sets and Knowledge Technology, RSKT 2011, held in Banff, Canada, in September 2011. The 89 revised full papers presented together with 3 keynote lectures and 1 invited tutorial session were carefully reviewed and selected from 229 submissions. The papers are organized in topical sections on attribute reduction and feature selection, generalized rough set models, machine learning with rough and hybrid techniques, knowledge technology and intelligent systems and applications.

This book constitutes the refereed proceedings of the International Joint Conference on Rough Sets, IJCRS 2016, held in Santiago de Chile, Chile, in October 2016. The 46 revised full papers presented together with 7 keynotes, tutorials and expert papers were carefully reviewed and selected from 108 submissions. The papers are grouped in topical sections on Rough Sets, Approximation and Granulation; Rough Sets, Non-Determinism and Incompleteness; Rough Sets and Three-way Decisions; Fuzziness and Similarity in Knowledge Representation; Machine Learning and Decision Making; Ranking and Clustering; Derivation and Application of Rules and Trees; Derivation and Application of Feature Subsets.

This book constitutes the refereed proceedings of the Fourth International Conference on Rough Sets and Knowledge Technology, RSKT 2009, held in Gold Coast, Australia, in July 2009. The 85 revised full papers papers presented together with 3 keynote papers and 2 special sessions were carefully reviewed and selected from 229 submissions. The papers are organized in topical sections on rough sets and computing, rough sets and data reduction, data mining and knowledge discovery, granular computing and cognitive computing, fuzzy sets and computing, knowledge technology and intelligent systems, computational intelligence and applications, image processing and understanding, and formal concept analysis.

This LNAI 11499 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2019, held in Debrecen, Hungary, in June 2019. The 41 full papers were carefully reviewed and selected from 71 submissions. The IJCRS conferences aim at bringing together experts from universities and research centers as well as the industry representing fields of research in which theoretical and applicational aspects of rough set theory already find or may potentially find usage. The papers are grouped in topical sections on core rough set models and methods; related methods and hybridization; areas of application.

This book constitutes the thoroughly refereed conference proceedings of the 10th International Conference on Rough Sets and Knowledge Technology, RSKT 2015, held in Tianjin, China, in November 2015, as part of the International Joint Conference on Rough Sets, IJCRS 2015, together with the 15th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDgrC 2015. The 66 papers presented at IJCRS 2015 were carefully reviewed and selected from 97 submissions. The 38 papers included in this volume are organized in the following topical sections: rough sets: the experts speak; reducts and rules; three-way decisions; logic and algebra; clustering; rough sets and graphs; and modeling and learning. In addition the volume contains 6 contributions by new fellows of the International Rough Set Society, an invited talk and a tutorial.