Lech Polkowski

Sankar Kumar Pal

Soft computing comprises various paradigms dedicated to approximately solving real-world problems, e.g. in decision making, classification or learning; among these paradigms are fuzzy sets, rough sets, neural networks, genetic algorithms, and others. It is well understood now in the soft computing community that hybrid approaches combining various paradigms are very promising approaches for solving complex problems. Exploiting the potential and strength of both neural networks and rough sets, this book is devoted to rough-neuro computing which is also related to the novel aspect of computing based on information granulation, in particular to computing with words. It provides foundational and methodological issues as well as applications in various fields.

Techniques for Computing with Words

Rough-Neural Computing

Ewa Orlowska

James F. Peters

Jerzy Grzymala-Busse

Ivo Düntsch

Annotation 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. Volume VI of the Transactions on Rough Sets (TRS) commemorates the life and work of Zdzislaw Pawlak (1926-2006). His legacy is rich and varied. Prof. Pawlak's research contributions have had far-reaching implications inasmuch as his works are fundamental in establishing new perspectives for scientific research in a wide spectrum of fields. This volume of the TRS presents papers that reflect the profound influence of a number of research initiatives by Professor Pawlak. In particular, this volume introduces a number of new advances in the foundations and applications of artificial intelligence, engineering, logic, mathematics, and science. These advances have significant implications in a number of research areas such as the foundations of rough sets, approximate reasoning, bioinformatics, computational intelligence, cognitive science, data mining, information systems, intelligent systems, machine intelligence, and security.

Commemorating Life and Work of Zdislaw Pawlak

Transactions on Rough Sets VI

This volume of the Transactions on Rough Sets commemorates the life and work of Zdzislaw Pawlak (1926-2006), whose legacy is rich and varied. It presents papers that reflect the profound influence of a number of research initiatives by Professor Pawlak, introducing a number of new advances in the foundations and applications of artificial intelligence, engineering, logic, mathematics, and science.

Commemorating Life and Work of Zdislaw Pawlak, Part I

Shusaku Tsumoto

Peng Wen

Yuefeng Li

Yiyu Y. Yao

The Rough Sets and Knowledge Technology (RSKT) conferences serve as a - jor forum that brings researchers and industry practitioners together to discuss and deliberate on fundamental issues of knowledge processing and management and knowledge-intensive practical solutions in the current knowledge age. - perts from around the world meet annually to present state-of-the-art sci- ti?c results, to nurture academic and industrial interaction, and to promote collaborative research in rough sets and knowledge technology. The main theme of the RSKT conference is to explore the synergy between rough sets and - vanced knowledge technology and applications, including knowledge discovery, datamining,knowledgeprocessingandmanagement,granularcomputing,evo- tionary computing, biocomputing and bioinformatics, cognitive computing and cognitive informatics, natural and arti?cial intelligence, Web intelligence, c- plex systems, and many others. The ?rst RSKT conference was held in 2006 in Chongqing, P.R. China, f- lowed by RSKT 2007 in Toronto, Canada and RSKT 2008 in Chengdu, P.R. China. This volume contains the papers selected for presentation at the 4th - ternationalConferenceonRoughSetsandKnowledgeTechnology(RSKT2009), which was held during July 14-16 on the Gold Coast, Australia.

4th International Conference, RSKT 2009, Gold Coast, Australia, July 14-16, 2009, Proceedings

Rough Sets and Knowledge Technology

This volume constitutes the refereed proceedings of the First International Conference on Rough Sets and Current Trends in Computing, RSCTC'98, held in Warsaw, Poland, in June 1998. The volume presents 82 revised papers carefully selected for inclusion in the proceedings; also included are five invited contributions. The volume is divided in topical sections on rough set methods, statistical inference, grammar systems and molecular computations, logic in rough sets, intelligent control, rough sets in knowledge discovery and data discovery, data mining, evolutionary computation, hybrid methods, etc..

First International Conference, RSCTC’98 Warsaw, Poland, June 22–26, 1998 Proceedings

Rough Sets and Current Trends in Computing

The monograph offers a view on Rough Mereology, a tool for reasoning under uncertainty, which goes back to Mereology, formulated in terms of parts by Lesniewski, and borrows from Fuzzy Set Theory and Rough Set Theory ideas of the containment to a degree. The result is a theory based on the notion of a part to a degree. One can invoke here a formula Rough: Rough Mereology : Mereology = Fuzzy Set Theory : Set Theory. As with Mereology, Rough Mereology finds important applications in problems of Spatial Reasoning, illustrated in this monograph with examples from Behavioral Robotics. Due to its involvement with concepts, Rough Mereology offers new approaches to Granular Computing, Classifier and Decision Synthesis, Logics for Information Systems, and are--formulation of well--known ideas of Neural Networks and Many Agent Systems. All these approaches are discussed in this monograph. To make the exposition self--contained, underlying notions of Set Theory, Topology, and Deductive and Reductive Reasoning with emphasis on Rough and Fuzzy Set Theories along with a thorough exposition of Mereology both in Lesniewski and Whitehead--Leonard--Goodman--Clarke versions are discussed at length. It is hoped that the monograph offers researchers in various areas of Artificial Intelligence a new tool to deal with analysis of relations among concepts.

An Introduction to Rough Mereology

Approximate Reasoning by Parts

Didier Dubois

Masahiro Inuiguchi

The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, starting 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 second volume of the Transactions on Rough Sets presents 17 thoroughly reviewed revised papers devoted to rough set theory, fuzzy set theory; these papers highlight important aspects of these theories, their interrelation and application in various fields.

Rough Sets and Fuzzy Sets

Transactions on Rough Sets II

Tsau Y. Lin

Rough set approach to reasoning under uncertainty is based on inducing knowledge representation from data under constraints expressed by discernibility or, more generally, similarity of objects. Knowledge derived by this approach consists of reducts, decision or association rules, dependencies, templates, or classifiers. This monograph presents the state of the art of this area. The reader will find here a deep theoretical discussion of relevant notions and ideas as well as rich inventory of algorithmic and heuristic tools for knowledge discovery by rough set methods. An extensive bibliography will help the reader to get an acquaintance with this rapidly growing area of research.

New Developments in Knowledge Discovery in Information Systems

Rough Set Methods and Applications

Beata Zielosko

Davide Ciucci

Yiyu Yao

Piotr Artiemjew

Dominik Ślęzak

Dun Liu

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).

International Joint Conference, IJCRS 2017, Olsztyn, Poland, July 3–7, 2017, Proceedings, Part I

Rough Sets

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.

A comprehensive introduction to mathematical structures essential for Rough Set Theory. The book enables the reader to systematically study all topics of rough set theory. After a detailed introduction in Part 1 along with an extensive bibliography of current research papers. Part 2 presents a self-contained study that brings together all the relevant information from respective areas of mathematics and logics. Part 3 provides an overall picture of theoretical developments in rough set theory, covering logical, algebraic, and topological methods. Topics covered include: algebraic theory of approximation spaces, logical and set-theoretical approaches to indiscernibility and functional dependence, topological spaces of rough sets. The final part gives a unique view on mutual relations between fuzzy and rough set theories (rough fuzzy and fuzzy rough sets). Over 300 excercises allow the reader to master the topics considered. The book can be used as a textbook and as a reference work.

Mathematical Foundations

This book presents a study in knowledge discovery in data with knowledge understood as a set of relations among objects and their properties. Relations in this case are implicative decision rules and the paradigm in which they are induced is that of computing with granules defined by rough inclusions, the latter introduced and studied within rough mereology, the fuzzified version of mereology. In this book basic classes of rough inclusions are defined and based on them methods for inducing granular structures from data are highlighted. The resulting granular structures are subjected to classifying algorithms, notably k—nearest neighbors and bayesian classifiers. Experimental results are given in detail both in tabular and visualized form for fourteen data sets from UCI data repository. A striking feature of granular classifiers obtained by this approach is that preserving the accuracy of them on original data, they reduce substantially the size of the granulated data set as well as the set of granular decision rules. This feature makes the presented approach attractive in cases where a small number of rules providing a high classification accuracy is desirable. As basic algorithms used throughout the text are explained and illustrated with hand examples, the book may also serve as a textbook.

An Application of Rough Mereology

Granular Computing in Decision Approximation

The papers on rough set theory and its applications placed in this volume present a wide spectrum of problems representative to the present. stage of this theory. Researchers from many countries reveal their rec.ent results on various aspects of rough sets. The papers are not confined only to mathematical theory but also include algorithmic aspects, applications and information about software designed for data analysis based on this theory. The volume contains also list of selected publications on rough sets which can be very useful to every one engaged in research or applications in this domain and sometimes perhaps unaware of results of other authors. The book shows that rough set theory is a vivid and vigorous domain with serious results to its credit and bright perspective for future developments. It lays on the crossroads of fuzzy sets, theory of evidence, neural networks, Petri nets and many other branches of AI, logic and mathematics. These diverse connec tions seem to be a very fertile feature of rough set theory and have essentially contributed to its wide and rapid expansion. It is worth mentioning that its philosophical roots stretch down from Leibniz, Frege and Russell up to Popper. Therefore many concepts dwelled on in rough set theory are not entirely new, nevertheless the theory can be viewed as an independent discipline on its own rights. Rough set theory has found many interesting real life applications in medicine, banking, industry and others.

Lech Polkowski

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