Granular, Fuzzy, and Soft Computing

The first edition of the Encyclopedia of Complexity and Systems Science (ECSS, 2009) presented a comprehensive overview of granular computing (GrC) broadly divided into several categories: Granular computing from rough set theory, Granular Computing in Database Theory, Granular Computing in Social Networks, Granular Computing and Fuzzy Set Theory, Grid/Cloud Computing, as well as general issues in granular computing. In 2011, the formal theory of GrC was established, providing an adequate infrastructure to support revolutionary new approaches to computer/data science, including the challenges presented by so-called big data.
For this volume of ECSS, Second Edition, many entries have been updated to capture these new developments, together with new chapters on such topics as data clustering, outliers in data mining, qualitative fuzzy sets, and information flow analysis for security applications. Granulations can be seen as a natural and ancient methodology deeply rooted in the human mind. Many daily things are routinely granulated into sub things: The topography of earth is granulated into hills, plateaus, etc., space and time are granulated into infinitesimal granules, and a circle is granulated into polygons of infinitesimal sides. Such granules led to the invention of calculus, topology and non-standard analysis. Formalization of general granulation was difficult but, as shown in this volume, great progress has been made in combing discrete and continuous mathematics under one roof for a broad range of applications in data science.

《複雜性與系統科學百科全書》（ECSS，2009年）的第一版提供了對粒狀計算（GrC）的全面概述，該概述被廣泛分為幾個類別：從粗糙集理論到粒狀計算、數據庫理論中的粒狀計算、社交網絡中的粒狀計算、模糊集理論中的粒狀計算、網格/雲計算以及粒狀計算中的一般問題。2011年，GrC的形式理論被建立起來，為支持計算機/數據科學的革命性新方法提供了適當的基礎，包括所謂的大數據所帶來的挑戰。

在這本《ECSS》第二版中，許多條目已經更新以反映這些新發展，並新增了關於數據聚類、數據挖掘中的異常值、質性模糊集以及安全應用中的信息流分析等主題的新章節。粒狀化可以被視為一種根植於人類思維中的自然而古老的方法論。許多日常事物都被例行地細分為子事物：地球的地形被細分為山丘、高原等，空間和時間被細分為無窮小的顆粒，圓被細分為無窮小邊的多邊形。這些顆粒導致了微積分、拓撲學和非標準分析的發明。對於一般粒狀化的形式化一直很困難，但正如本書所示，已經在將離散和連續數學結合在一個框架下取得了巨大進展，以應用於數據科學的廣泛領域。

Tsau-Young Lin holds a Ph.D. from Yale University and is Professor of Computer Science at San Jose State University. He has published over 250 papers and has edited a number of books. Prof. Lin coined the term Granular Computing (GrC) and has researched the subject for the past two decades. He is Founding President of the Rough Set Society and President of the GrC Society. His areas of expertise include data science (deep data analysis, data/knowledge mining, uncertainty), topology-based computing (algebraic, geometric, point set), granular and rough computing, and cyber security.

Churn-Jung Liau received a B.S., an M.S. and a Ph.D in computer science and information engineering from National Taiwan University in 1985, 1987 and 1992 respectively. He then joined the Institute of Information Science, Academia Sinica, Taiwan and is currently a tenured full research fellow. His major research interest includes aaplied logic, artificial intelligence, and uncertainty reasoning.

Janusz Kacprzyk is Professor of Computer Science at the Systems Research Institute, Polish Academy of Sciences, WIT - Warsaw School of Information Technology, and Chongqing Three Gorges University, Wanzhou, Chinqgqung, China, and Professor of Automatic Control at PIAP - Industrial Institute of Automation and Measurements. He is Honorary Foreign Professor at the Department of Mathematics, Yli Normal University, Xinjiang, China. He is Full Member of the Polish Academy of Sciences, Member of Academia Europaea, European Academy of Sciences and Arts, European Academy of Sciences, Foreign Member of the: Bulgarian Academy of Sciences, Spanish Royal Academy of Economic and Financial Sciences (RACEF), Finnish Society of Sciences and Letters, and Flemish Royal Academy of Belgium of Sciences and the Arts (KVAB). He was awarded with 4 honorary doctorates. He is Fellow of IEEE, IET, IFSA, EurAI and SMIA.

His main research interests include the use of modern computation computational and artificial intelligence tools, notably fuzzy logic, in systems science, decision making, optimization, control, data analysis and data mining, with applications in mobile robotics, systems modeling, ICT etc.

He authored 7 books, (co)edited more than 100 volumes, (co)authored more than 600 papers, including ca. 80 in journals indexed by the WoS. His bibliographic data are: Google Scholar: citations: 28094; h-index: 74, Scopus: citations: citations: 8416; h-index: 40, ResearcherID (M-9574-2014): citations: 9014; h-index=42 and Web of Science: citations: 6696 (5517 without self-citations) h-index: 34.

He is the editor in chief of 7 book series at Springer, and of 2 journals, and is on the editorial boards of ca. 40 journals.. He is President of the Polish Operational and Systems Research Society and Past President of International Fuzzy Systems Association.

林朝永擁有耶魯大學的博士學位，現任職於聖荷西州立大學的計算機科學教授。他已發表超過250篇論文並編輯了多本書籍。林教授創造了「顆粒計算」（GrC）一詞並在過去二十年中進行了相關研究。他是粗糙集學會的創始會長和顆粒計算學會的會長。他的專業領域包括數據科學（深度數據分析、數據/知識挖掘、不確定性）、基於拓撲的計算（代數、幾何、點集）、顆粒和粗糙計算以及網絡安全。

廖俊榮於1985年、1987年和1992年分別在國立台灣大學獲得學士、碩士和博士學位，並加入台灣中央研究院資訊科學研究所，目前擔任終身研究員。他的主要研究興趣包括應用邏輯、人工智能和不確定性推理。

Janusz Kacprzyk是波蘭科學院系統研究所、華沙資訊技術學院和重慶三峽大學的計算機科學教授，同時也是波蘭工業自動化和測量研究所的自動控制教授。他是新疆伊犁師範大學數學系的榮譽外國教授。他是波蘭科學院的正式會員，歐洲科學與藝術學院、歐洲科學學院、保加利亞科學院、西班牙皇家經濟和金融科學院（RACEF）、芬蘭科學與文學學會以及佛蘭芒皇家比利時科學和藝術學院（KVAB）的外籍會員。他獲得了4個榮譽博士學位。他是IEEE、IET、IFSA、EurAI和SMIA的會士。

他的主要研究興趣包括在系統科學、決策、優化、控制、數據分析和數據挖掘等領域中使用現代計算和人工智能工具，尤其是模糊邏輯，並應用於移動機器人、系統建模和信息通信技術等領域。

他撰寫了7本書籍，編輯了100多本專著，共同撰寫了600多篇論文，其中約80篇被WoS索引的期刊收錄。他的學術數據如下：Google Scholar：引用次數：28094；h指數：74，Scopus：引用次數：8416；h指數：40，ResearcherID（M-9574-2014）：引用次數：9014；h指數：42，Web of Science：引用次數：6696（自引用除外）；h指數：34。

他是Springer出版社的7個書系的主編，也是2本期刊的主編，並擔任約40本期刊的編輯委員會成員。他是波蘭運籌學和系統研究學會的主席，也是國際模糊系統協會的前任主席。