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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 thoroughly refereed conference proceedings of the 14th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDGrC 2013, held in Halifax, Canada in October 2013 as one of the co-located conference of the 2013 Joint Rough Set Symposium, JRS 2013. The 69 papers (including 44 regular and 25 short papers) included in the JRS proceedings (LNCS 8170 and LNCS 8171) were carefully reviewed and selected from 106 submissions. The papers in this volume cover topics such as inconsistency, incompleteness, non-determinism; fuzzy and rough hybridization; granular computing and covering-based rough sets; soft clustering; image and medical data analysis.

This book constitutes the refereed proceedings of the 7th International Conference on Rough Sets and Knowledge Technology, RSKT 2012, held in Chengdu, China during August 2012, as one of the co-located conferences of the 2012 Joint Rough Set Symposium, JRS 2012. The 63 revised papers (including 42 regular and 21 short papers) were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on rough sets and its generalizations, rough sets in data and knowledge processing, knowledge technology, advances in granular computing (AGC 2012 workshop), decision-theoretic rough set model and applications (special session), intelligent decision making and granular computing (special session), rough set foundations (special session).

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.

The two-volume set (LNCS 6728 and 6729) constitutes the refereed proceedings of the International Conference on Swarm Intelligence, ICSI 2011, held in Chongqing, China, in June 2011. The 143 revised full papers presented were carefully reviewed and selected from 298 submissions. The papers are organized in topical sections on theoretical analysis of swarm intelligence algorithms, particle swarm optimization, applications of pso algorithms, ant colony optimization algorithms, bee colony algorithms, novel swarm-based optimization algorithms, artificial immune system, differential evolution, neural networks, genetic algorithms, evolutionary computation, fuzzy methods, and hybrid algorithms - for part I. Topics addressed in part II are such as multi-objective optimization algorithms, multi-robot, swarm-robot, and multi-agent systems, data mining methods, machine learning methods, feature selection algorithms, pattern recognition methods, intelligent control, other optimization algorithms and applications, data fusion and swarm intelligence, as well as fish school search - foundations and applications.

The two-volume set (LNCS 6728 and 6729) constitutes the refereedproceedings of the International Conference on Swarm Intelligence, ICSI2011, held in Chongqing, China, in June 2011.The 143 revised full papers presented were carefully reviewed and selected from 298 submissions. The papers are organized in topical sections on theoretical analysis of swarm intelligence algorithms, particle swarm optimization, applications of pso algorithms, ant colony optimization algorithms, bee colony algorithms, novel swarm-based optimization algorithms, artificial immune system, differential evolution, neural networks, genetic algorithms, evolutionary computation, fuzzy methods, and hybrid algorithms - for part I. Topics addressed in part II are such as multi-objective optimization algorithms, multi-robot, swarm-robot, and multi-agent systems, data mining methods, machine learning methods, feature selection algorithms, pattern recognition methods, intelligent control, other optimization algorithms and applications, data fusion and swarm intelligence, as well as fish school search - foundations and applications.

TheInternationalConferenceonRoughSetandKnowledgeTechnology(RSKT) has been held every year since 2006. RSKT serves as a major forum that brings researchers and industry practitioners together to discuss and deliberate on fundamental issues of knowledge processing and management and knowled- intensive practical solutions in the current knowledge age. Experts from around the world meet to present state-of-the-art scienti?c results, to nurture academic and industrial interaction, and to promote collaborative research in rough sets and knowledge technology. The?rst RSKT was held in Chongqing, China, f- lowed by RSKT 2007 in Toronto, Canada, RSKT 2008 in Chengdu, China and RSKT 2009 in Gold Coast, Australia. RSKT 2010, the 5th in the series, was held in Beijing, China, October 15–17, 2010. This volume contains 98 papers selected for presentation at RSKT 2010. Following the success of the previous conferences, RSKT 2010 continued the tradition of a very rigorous reviewing process. Every submission was reviewed byatleasttworeviewers.Moreover,RSKT2010invitedseveralareachairsto- pervise the review process of every submission. Most submissions were reviewed by three experts. The Program Committee members were deeply involved in a highly engaging selection process with discussions among reviewers and area chairs. When necessary, additional expert reviews were sought. As a result, only top-quality papers were chosen for presentation at the conference, including 49 regular papers (acceptance rate of 28%) and 25 short papers (acceptance rate of 14.3%). We would like to thank all the authors for contributing their best papers. Without their support, this conference would not have been possible.

The denotational and expressive needs in cognitive informatics, computational intelligence, software engineering, and knowledge engineering have led to the development of new forms of mathematics collectively known as denotational mathematics. Denotational mathematics is a category of mathematical structures that formalize rigorous expressions and long-chain inferences of system compositions and behaviors with abstract concepts, complex relations, and dynamic processes. Typical paradigms of denotational mathematics are concept algebra, system algebra, Real-Time Process Algebra (RTPA), Visual Semantic Algebra (VSA), fuzzy logic, and rough sets. A wide range of applications of denotational mathematics have been identified in many modern science and engineering disciplines that deal with complex and intricate mathematical entities and structures beyond numbers, Boolean variables, and traditional sets. This issue of Springer's Transactions on Computational Science on Denotational Mathematics for Computational Intelligence presents a snapshot of current research on denotational mathematics and its engineering applications. The volume includes selected and extended papers from two international conferences, namely IEEE ICCI 2006 (on Cognitive Informatics) and RSKT 2006 (on Rough Sets and Knowledge Technology), as well as new contributions. The following four important areas in denotational mathem- ics and its applications are covered: Foundations and applications of denotational mathematics, focusing on: a) c- temporary denotational mathematics for computational intelligence; b) deno- tional mathematical laws of software; c) a comparative study of STOPA and RTPA; and d) a denotational mathematical model of abstract games.

This volume contains the papers selected for presentation at the Third Inter- tional Conference on Rough Sets and Knowledge Technology (RSKT 2008) held in Chengdu, P. R. China, May 16–19, 2008. The RSKT conferences were initiated in 2006 in Chongqing, P. R. China. RSKT 2007 was held in Toronto, Canada, together with RSFDGrC 2007, as JRS 2007. The RSKT conferences aim to present state-of-the-art scienti?c - sults, encourage academic and industrial interaction, and promote collaborative research in rough sets and knowledge technology worldwide. They place emphasis on exploring synergies between rough sets and knowledge discovery, knowledge management, data mining, granular and soft computing as well as emerging application areas such as bioinformatics, cognitive informatics, and Web intel- gence, both at the level of theoretical foundations and real-life applications. RSKT 2008 focused on?ve major research?elds: computing theory and paradigms, knowledge technology, intelligent information processing, intelligent control, and applications. This was achieved by including in the conference program sessions on rough and soft computing, rough mereology with app- cations, dominance-based rough set approach, fuzzy-rough hybridization, gr- ular computing, logical and mathematical foundations, formal concept analysis, data mining, machine learning, intelligent information processing, bioinform- ics and cognitive informatics, Web intelligence, pattern recognition, and real-life applications of knowledge technology. A very strict quality control policy was adopted in the paper review process of RSKT 2008. Firstly, the PC Chairs - viewed all submissions.

This volume contains the papers selected for presentation at the 9th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2003) held at Chongqing University of Posts and Telecommunications, Chongqing, P.R. China, May 26–29, 2003. There were 245 submissions for RSFDGrC 2003 excluding for 2 invited keynote papers and 11 invited plenary papers. Apart from the 13 invited papers, 114 papers were accepted for RSFDGrC 2003 and were included in this volume. The acceptance rate was only 46.5%. These papers were divided into 39 regular oral presentation papers (each allotted 8 pages), 47 short oral presentation papers (each allotted 4 pages) and 28 poster presentation papers (each allotted 4 pages) on the basis of reviewer evaluations. Each paper was reviewed by three referees. The conference is a continuation and expansion of the International Workshops on Rough Set Theory and Applications. In particular, this was the ninth meeting in the series and the first international conference. The aim of RSFDGrC2003 was to bring together researchers from diverse fields of expertise in order to facilitate mutual understanding and cooperation and to help in cooperative work aimed at new hybrid paradigms. It is our great pleasure to dedicate this volume to Prof. Zdzislaw Pawlak, who first introduced the basic ideas and definitions of rough sets theory over 20 years ago.