This special book is dedicated to the memory of Professor Zdzislaw Pawlak, the father of rough set theory, in order to commemorate both the 10th anniversary of his passing and 35 years of rough set theory. The book consists of 20 chapters distributed into four sections, which focus in turn on a historical review of Professor Zdzislaw Pawlak and rough set theory; a review of the theory of rough sets; the state of the art of rough set theory; and major developments in rough set based data mining approaches. Apart from Professor Pawlak's contributions to rough set theory, other areas he was interested in are also included. Moreover, recent theoretical studies and advances in applications are also presented. The book will offer a useful guide for researchers in Knowledge Engineering and Data Mining by suggesting new approaches to solving the problems they encounter.

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 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.

In this book, the following three approaches to data analysis are presented:

- Test Theory, founded by Sergei V. Yablonskii (1924-1998); the first publications appeared in 1955 and 1958,

- Rough Sets, founded by Zdzis aw I. Pawlak (1926-2006); the first publications appeared in 1981 and 1982,

- Logical Analysis of Data, founded by Peter L. Hammer (1936-2006); the first publications appeared in 1986 and 1988.

These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected.

- Logical Analysis of Data, founded by Peter L. Hammer (1936-2006); the first publications appeared in 1986 and 1988.

These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected.

These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected."

This book presents novel approaches to the formal specification of concurrent and parallel systems, mathematical models for describing such systems, and programming and verification concepts for their implementation. A special emphasis is on methods based on artificial intelligence and machine learning techniques. Chapters are revised selected papers from the 29th International Workshop on Concurrency, Specification, and Programming (CS&P 2021), Berlin, Germany. Nine independent chapters cover formal approaches to topics such as requirements formalization, parsing, or granular computing, as well as their applications in recommender systems, decision making, security, optimization, and other areas. The book thus addresses both researchers and practitioners in its field.

Since the emergence of the formal concept of probability theory in the seventeenth century, uncertainty has been perceived solely in terms of probability theory. However, this apparently unique link between uncertainty and probability theory has come under investigation a few decades back. Uncertainties are nowadays accepted to be of various kinds. Uncertainty in general could refer to different sense like not certainly known, questionable, problematic, vague, not definite or determined, ambiguous, liable to change, not reliable. In Indian languages, particularly in Sanskrit-based languages, there are other higher levels of uncertainties. It has been shown that several mathematical concepts such as the theory of fuzzy sets, theory of rough sets, evidence theory, possibility theory, theory of complex systems and complex network, theory of fuzzy measures and uncertainty theory can also successfully model uncertainty.

This special book is dedicated to the memory of Professor Zdzislaw Pawlak, the father of rough set theory, in order to commemorate both the 10th anniversary of his passing and 35 years of rough set theory. The book consists of 20 chapters distributed into four sections, which focus in turn on a historical review of Professor Zdzislaw Pawlak and rough set theory; a review of the theory of rough sets; the state of the art of rough set theory; and major developments in rough set based data mining approaches. Apart from Professor Pawlak's contributions to rough set theory, other areas he was interested in are also included. Moreover, recent theoretical studies and advances in applications are also presented. The book will offer a useful guide for researchers in Knowledge Engineering and Data Mining by suggesting new approaches to solving the problems they encounter.

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 XIX in the series focuses on the current trends and advances in both the foundations and practical applications of rough sets. It contains 7 extended and revised papers originally presented at the Workshop on Rough Set Applications, RSA 2012, held in Wroclaw, Poland, in September 2012. In addition, the book features 3 contributions in the category of short surveys and monographs on the topic.

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 XVIII includes extensions of papers from the Joint Rough Set Symposium (JRS 2012), which was held in Chengdu, China, in August 2012. The seven papers that constitute this volume deal with topics such as: rough fuzzy sets, intuitionistic fuzzy sets, multi-granulation rough sets, decision-theoretic rough sets, three-way decisions and their applications in attribute reduction, feature selection, overlapping clustering, data mining, cost-sensitive learning, face recognition, and spam filtering.

In this book, the following three approaches to data analysis are presented: - Test Theory, founded by Sergei V. Yablonskii (1924-1998); the first publications appeared in 1955 and 1958, - Rough Sets, founded by Zdzislaw I. Pawlak (1926-2006); the first publications appeared in 1981 and 1982, - Logical Analysis of Data, founded by Peter L. Hammer (1936-2006); the first publications appeared in 1986 and 1988. These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected. - Logical Analysis of Data, founded by Peter L. Hammer (1936-2006); the first publications appeared in 1986 and 1988. These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected. These three approaches have much in common, but researchers active in one of these areas often have a limited knowledge about the results and methods developed in the other two. On the other hand, each of the approaches shows some originality and we believe that the exchange of knowledge can stimulate further development of each of them. This can lead to new theoretical results and real-life applications and, in particular, new results based on combination of these three data analysis approaches can be expected.

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 XVII is a continuation of a number of research streams which have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the 21st century. The research streams represented in the papers cover both theory and applications of rough, fuzzy and near sets as well as their combinations.

This book constitutes the refereed proceedings of the 9th International Conference on Active Media Technology, AMT 2013, held in Maebashi, Japan, in October 2013. The 26 revised full papers presented together with 2 short papers, 16 workshop papers, and 12 special session papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on active computer systems, interactive systems, and application of AMT based systems; active media machine learning and data mining techniques; AMT for semantic web, social networks, and cognitive foundations. Additionally, the main topic of the workshop papers is: intelligence for strategic foresight; and for the special session papers: technologies and theories of narrative; evolutionary computation and its application; and intelligent media search techniques.

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 XVI includes extensions of papers from the Rough Sets and Knowledge Technology Conference which was held in Banff, Canada, in October 2011. In addition this book contains a long paper based on a PhD thesis. The papers cover both theory and applications of rough, fuzzy and near sets. They offer a continuation of a number of research streams which have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the 21st century.

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 XV offers a number of research streams that have grown out of the seminal work by Zdzislaw Pawlak. The 4 contributions included in this volume presents a rough set approach in machine learning; the introduction of multi-valued near set theory; the advent of a complete system that supports a rough-near set approach to digital image analysis; and an exhaustive study of the mathematics of vagueness.

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."

Volume IX of the Transactions on Rough Sets (TRS) provides evidence of the continuing growth of a number of research streams that were either directly or indirectly begun by the seminal work on rough sets by Zdzis law Pawlak (1926- 1 2006) .OneoftheseresearchstreamsinspiredbyProf.Pawlakisroughset-based intelligent systems, a topic that was an important part of his early 1970s work on knowledge description systems prior to his discovery of rough sets during the early 1980s. Evidence of intelligent systems as a recurring motif over the past twodecadescanbefoundintherough-setliteraturethatnowincludesover4,000 2 publications by more than 1,600 authors in the rough set database . This volume of the TRS includes articles that are extensions of papers in- 3 cludedinthe?rstconferenceonRoughSetsandIntelligentSystemsParadigms . In addition to research on intelligent systems, this volume 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 and applications of arti?cial intelligence, engineering, image processing, logic, mathematics, medicine, music, and science. These advances have sign- icant implications in a number of research areas such as attribute reduction, approximation schemes, category-based inductive reasoning, classi?ers, classi- ing mappings, context algebras, data mining, decision attributes, decision rules, decision support, diagnostic feature analysis, EEG classi?cation, feature ana- sis, granular computing, hierarchical classi?ers, indiscernibility relations, inf- mationgranulation, informationsystems, musicalrhythm retrieval, probabilistic dependencies, reducts, rough-fuzzy C-means, rough inclusion functions, rou- ness, singing voice recognition, and vagueness. A total of 47 researchers are represented in this volu

VolumeVIIIoftheTransactions on Rough Sets (TRS)containsa widespectrum of contributions to the theory and applications of rough sets. The pioneering work by Prof. Zdzis law Pawlak led to the introduction of knowledge representation systems during the early 1970s and the discovery of rough sets during the early 1980s. During his lifetime, he nurtured worldwide interest in approximation, approximate reasoning, and rough set theory and its 1 applications . Evidence of the in?uence of Prof. Pawlak's work can be seen in the growth in the rough-set literature that now includes over 4000 publications 2 by more than 1900 authors in the rough set database as well as the growth and 3 maturity of the International Rough Set Society . This volume of TRS presents papers that introduce a number of new - vances in the foundations and applications of arti?cial intelligence, engineering, logic, mathematics, and science. These advances have signi?cant implications in a number of researchareas.In addition, it is evident from the papers included in this volume that roughset theoryand its application forma veryactiveresearch area worldwide. A total of 58 researchers from 11 countries are represented in this volume, namely, Australia, Canada, Chile, Germany, India, Poland, P.R. China, Oman, Spain, Sweden, and the USA. Evidence of the vigor, breadth, and depth of research in the theory and applications rough sets can be found in the articles in this volume. This volume contains 17 papers that explore a number of research streams.

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.

Together with volume VI of the Transactions on Rough Sets series, this book commemorates the life and work of Zdzislaw Pawlak (1926-2006). It presents papers that reflect the profound influence of a number of research initiatives by Professor Pawlak, introducing a number of advances in the foundations and applications of AI, engineering, logic, mathematics, and science, which have had significant implications in a number of research areas.

This book is dedicated to the monumental life, work and creative genius of Zdzislaw Pawlak, the originator of rough sets, who passed away in April 2006. It opens with a commemorative article that gives a brief coverage of Pawlak's works in rough set theory, molecular computing, philosophy, painting and poetry. Fifteen papers explore the theory of rough sets in various domains as well as new applications of rough sets.

Volume III of the Transactions on Rough Sets (TRS) introduces advances in the theory and application of rough sets. These advances have far-reaching impli- tions in a number of researchareas such as approximate reasoning, bioinform- ics, computerscience, datamining, engineering(especially, computerengineering and signal analysis), intelligent systems, knowledge discovery, pattern recog- tion, machineintelligence, andvariousformsoflearning. This volumerevealsthe vigor, breadth and depth in research either directly or indirectly related to the rough sets theory introduced by Prof. Zdzis law Pawlak more than three decades ago. Evidence of this can be found in the seminal paper on data mining by Prof. Pawlak included in this volume. In addition, there are eight papers on the theory and application of rough sets as well as a presentation of a new version of the Rough Set Exploration System (RSES) tool set and an introduction to the Rough Set Database System (RSDS). Prof. Pawlak has contributed a pioneering paper on data mining to this v- ume. In this paper, it is shown that information ?ow in a ?ow graph is governed by Bayes' rule with a deterministic rather than a probabilistic interpretation. A cardinal feature of this paper is that it is self-contained inasmuch as it not only introduces a new viewof information?owbut alsoprovidesanintroduction to the basic concepts of ?ow graphs. The representation of information ?ow - troduced in this paper makes it possible to study di?erent relationships in data and establishes a basis for a new mathematical tool for data mining. Inadditionto thepaperbyProf

This collection of articles is devoted to fuzzy as well as rough set theories. Both theoriesarebasedonrigorousideas, methodsandtechniquesinlogic, mathem- ics, and computer science for treating problems for which approximate solutions are possible only, due to their inherent ambiguity, vagueness, incompleteness, etc. Vast areas of decision making, data mining, knowledge discovery in data, approximatereasoning, etc., aresuccessfully exploredusing methods workedout within fuzzy and rough paradigms. By the very nature of fuzzy and rough paradigms, outlined above, they are related to distinct logical schemes: it is well-known that rough sets are related to modal logicsS5andS4(Orl owska, E., Modal logics in the theory of infor- tion systems, Z. Math. Logik Grund. Math. 30, 1984, pp. 213 ?.; Vakarelov, D., Modal logics for knowledgerepresentationsystems, LNCS 363,1989, pp. 257?.) and to ?nitely-valued logics (Pagliani, P., Rough set theory and logic-algebraic structures. In Incomplete Information: Rough Set Analysis, Orlo wska, E., ed., Physica/Springer, 1998, pp. 109 ?.; Polkowski, L. A note on 3-valued rough logic accepting decision rules, Fundamenta Informaticae 61, to appear). Fuzzy sets are related to in?nitely-valued logics (fuzzy membership to degree r? 0,1]expressingtruthdegreer)(Goguen, J.A., Thelogicofinexactconcepts, Synthese18/19,1968-9, pp.325?.;Pavelka, J., OnfuzzylogicI, II, III, Z. Math. Logik Grund. Math. 25, 1979, pp. 45 ?., pp. 119 ?., pp. 454 ?.; Dubois, D., Prade, H., Possibility Theory, Plenum Press, 1988; Haj ek, P., Metamathematics of Fuzzy Logic, Kluw

We would like to present, with great pleasure, the ?rst volume of a new jo- nal, Transactions on Rough Sets. This journal, part of the new journal subline in the Springer-Verlag series Lecture Notes in Computer Science, is devoted to the entire spectrum of rough set related issues, starting from logical and ma- ematical foundations of rough sets, through all aspects of rough set theory and its applications, 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, theory of evidence, etc. The ?rst, pioneering papers on rough sets, written by the originator of the idea, ProfessorZdzis lawPawlak, werepublishedintheearly1980s.Weareproud to dedicate this volume to our mentor, Professor Zdzis law Pawlak, who kindly enriched this volume with his contribution on philosophical, logical, and mat- matical foundations of roughset theory. In his paper Professor Pawlakshows all over again the underlying ideas of rough set theory as well as its relations with Bayes' theorem, con?ict analysis, ?ow graphs, decision networks, and decision rules.

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 XXIII in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.