Transactions on Computational Science II
This volume covers denotational mathematics for computational intelligence. It includes 12 papers that detail: foundations and applications of denotational mathematics, rough and fuzzy set theories, granular computing, and knowledge and information modeling.
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| Main Authors | , , , , |
|---|---|
| Format | eBook |
| Language | English |
| Published |
Berlin, Heidelberg
Springer Berlin / Heidelberg
2008
Springer Berlin Heidelberg Springer |
| Edition | 1 |
| Series | Lecture Notes in Computer Science |
| Subjects | |
| Online Access | Get full text |
| ISBN | 354087562X 9783540875628 |
| ISSN | 0302-9743 1611-3349 |
| DOI | 10.1007/978-3-540-87563-5 |
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| Abstract | This volume covers denotational mathematics for computational intelligence. It includes 12 papers that detail: foundations and applications of denotational mathematics, rough and fuzzy set theories, granular computing, and knowledge and information modeling. |
|---|---|
| AbstractList | 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 covers denotational mathematics for computational intelligence. It includes 12 papers that detail: foundations and applications of denotational mathematics, rough and fuzzy set theories, granular computing, and knowledge and information modeling. |
| Author | Wang, Guoyin Yao, Yiyu Y Kanade, Takeo Kittler, Josef Hutchison, David |
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| Copyright | Springer-Verlag Berlin Heidelberg 2008 |
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| DOI | 10.1007/978-3-540-87563-5 |
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| Discipline | Sciences (General) Computer Science |
| EISBN | 9783540875635 3540875638 |
| EISSN | 1611-3349 |
| Edition | 1 2008 edition. |
| Editor | Wang, Guoyin Tan, C. J. Kenneth Gavrilova, Marina L. Yao, Yiyu Wang, Yingxu |
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| RelatedPersons | Kleinberg, Jon M. Mattern, Friedemann Nierstrasz, Oscar Steffen, Bernhard Kittler, Josef Vardi, Moshe Y. Weikum, Gerhard Sudan, Madhu Naor, Moni Mitchell, John C. Terzopoulos, Demetri Pandu Rangan, C. Kanade, Takeo Hutchison, David Tygar, Doug |
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| Snippet | This volume covers denotational mathematics for computational intelligence. It includes 12 papers that detail: foundations and applications of denotational... The denotational and expressive needs in cognitive informatics, computational intelligence, software engineering, and knowledge engineering have led to the... |
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| SubjectTerms | Computational Science and Engineering Computer Science Data processing Mathematics of Computing Science Science-Data processing Software Engineering/Programming and Operating Systems Theory of Computation |
| TableOfContents | Intro -- Preface -- Table of Contents -- Perspectives on Denotational Mathematics: New Means of Thought -- On Contemporary Denotational Mathematics for Computational Intelligence -- Mereological Theories of Concepts in Granular Computing -- On Mathematical Laws of Software -- Rough Logic and Its Reasoning -- On Reduct Construction Algorithms -- Attribute Set Dependence in Reduct Computation -- A General Model for Transforming Vague Sets into Fuzzy Sets -- Quantifying Knowledge Base Inconsistency Via Fixpoint Semantics -- Contingency Matrix Theory I: Rank and Statistical Independence in a Contigency Table -- Applying Rough Sets to Information Tables Containing Possibilistic Values -- Toward a Generic Mathematical Model of Abstract Game Theories -- A Comparative Study of STOPA and RTPA -- Author Index Time Complexity Analysis -- Conclusion -- References -- Attribute Set Dependence in Reduct Computation -- Introduction -- Preliminaries -- Discernibility and Dependency -- Algorithm Overview -- Candidate Set Generation -- Pruning with Subsets -- Finding Dependent Sets -- Finding Reducts -- Execution Example -- Algorithm Analysis -- Implementation Details -- Algorithm Execution Example -- Complexity Analysis -- Data Structures for Storing Attribute Set Collections -- Pruning Efficiency Testing -- ExecutionTimeTesting -- Summary -- References -- A General Model for Transforming Vague Sets into Fuzzy Sets -- Introduction -- Vague Set -- Related Methods for Transforming Vague Sets into Fuzzy Sets -- A General Model for Transforming Vague Sets into Fuzzy Sets -- Case Study for the General Transformation Model -- Conclusion -- References -- Quantifying Knowledge Base Inconsistency Via Fixpoint Semantics -- Introduction -- Related Work -- Overview of KB Fixpoint Semantics -- KB Coherence -- Significance Measure of Inconsistency -- Discussions and Comparison -- Conclusion -- References -- Contingency Matrix Theory I: Rank and Statistical Independence in a Contigency Table -- Introduction -- Contingency Tables -- Rough Sets Notations -- Contingency Table (2 \times 2) -- Contingency Table \(m\times n) -- Statistical Independence in 2\{times} 2 Contingency Table -- Statistical Independence in 2\{times}3 Contingency Table -- Statistical Independence in m{\times} n Contingency Table -- Statistical Independence with m-Way Tables -- Three-Way Table -- Multi-way Table -- Contingency Matrix -- Independence of 2 {\times} 2 Contingency Table -- Independence of 3 {\times} 3 Contingency Table -- Independence of m{\times} n Contingency Table -- Pseudo Statistical Independence: Example -- Three-Way Contingency Table (Rank: 2) Four-Way Contingency Table (Rank: 3) -- Four-Way Contingency Table (Rank: 2) -- Pseudo Statiatical Independence -- Conclusion -- References -- Applying Rough Sets to Information Tables Containing Possibilistic Values -- Introduction -- Rough Sets under Precise Information -- Methods of Possible Worlds -- Applying Rough Sets to Information Tables Containing Possibilistic Values -- Information Tables Containing Missing Values -- Conclusions -- References -- Toward a Generic Mathematical Model of Abstract Game Theories -- Introduction -- Related Work -- The Generic Mathematical Model of Abstract Games -- The Formal Model of Abstract Games -- Properties of Abstract Games -- Behaviors of Abstract Games -- Behaviors of Zero-Sum Games -- Behaviors of Nonzero-Sum Games -- Strategies of Decision Making in Games -- The Maximin Strategy in Games -- The Maximum Utility Strategy in Games -- Conclusions -- References -- A Comparative Study of \STOPA and \RTPA -- Introduction -- The Language \RTPA -- The Language \STOPA -- Process Relations in \STOPA -- The Memorizing Process -- Encoding Process -- Storage Process -- Retrieval Process -- Formal Description of the Memorizing Process -- Conclusions -- References -- Author Index Intro -- Title -- Preface -- Table of Contents -- Perspectives on Denotational Mathematics: New Means of Thought -- Introduction -- What Is Denotational Mathematics? -- Why Denotational Mathematics Is Needed? -- References -- On Contemporary Denotational Mathematics for Computational Intelligence -- Introduction -- The Emergence and Development of Denotational Mathematics -- Fundamental Elements in Modeling Cognitive and Intelligent Systems -- New Problems Require New Forms of Mathematics -- The Domain and Architecture of Denotational Mathematics -- Paradigms of Denotational Mathematics -- Concept Algebra -- System Algebra -- Real-Time Process Algebra (RTPA) -- Applications of Denotational Mathematics -- The Big-R Notation of RTPA for Modeling Iterative and Recursive System Architectures and Behaviors -- Autonomous Machine Learning Using Concept Algebra -- Granular Computing Using System Algebra -- Conclusions -- References -- Mereological Theories of Concepts in Granular Computing -- Introduction: On the Notions of a Concept, Knowledge and Reasoning -- Mathematical Approaches to the Notion of a Concept -- Rough Mereology -- Granulation of Knowledge -- Metric-induced Rough Inclusions -- Rough Inclusions Induced by Means of Representations of Entities: The Attribute-Value Formalism -- Archimedean t-Norms in Inducing Rough Inclusions -- The Case of Residual Implication-Induced Rough Inclusions -- Granular Topologies -- Rough Inclusions on Finite Sets -- Approximate Reasoning: A Granular Rough Mereological Logic GRML -- The Case of the Archimedean t-Norm \L of \LUkasiewicz -- On Applications of Rough Inclusions and Granulation in Computer Science -- References -- On Mathematical Laws of Software -- Introduction -- The Algebraic Treatment of Fundamental Behaviors of Software Systems in RTPA The Generic Mathematical Model of Programs and Software Systems -- The Type System of RTPA -- The Meta-processes of Software Behaviors in RTPA -- Process Operations of RTPA -- Laws of Meta-processes of Software Behaviors -- Laws of Assignments -- Laws of Evaluations -- Laws of Addressing -- Laws of I/O Manipulations -- Laws of Skip -- Laws of Algebraic Operations of Software Behaviors -- Laws of Sequential Processes -- Laws of Jump Processes -- Laws of Branch Processes -- Laws of Switch Processes -- Laws of Iterative Processes -- Laws of Recursive Processes -- Laws of Function Calls -- Laws of Parallel Processes -- Laws of Concurrent Processes -- Laws of Interleave Processes -- Conclusions -- References -- Rough Logic and Its Reasoning -- Introduction -- Basic Concepts of Rough Logic -- Well-Formed Formulae in the Rough Logic -- Interpretation and Assignment in the Rough Logic -- Truth Values of Rough Logical Formulae -- Semantics Model of Rough Logic -- Related Properties of Rough Logic -- Clause Forms of Rough Logical Formulae -- Deductive Reasoning of the Rough Logical Formulae -- Resolution Reasoning of the Rough Logical Formulae -- Resolution Principles -- \lambda-Resolution Strategies of the Rough Logic -- Applications of Rough Logic to Problem Resolving in AI -- Perspective of Studying for the Rough Logic -- References -- On Reduct Construction Algorithms -- Introduction -- Feature Selection and Reduct Construction -- Basic Concepts and Notations -- Information Table and Attribute Lattice -- Equivalence Relations -- Discernibility Matrices -- Reducts -- Reduct Construction by Deletion -- Control Strategy -- Attribute Selection Heuristics -- Reduct Construction by Addition-Deletion -- Control Strategy -- Attribute Selection Heuristics -- Reduct Construction by Addition -- Control Strategy -- Attribute Selection Heuristics |
| Title | Transactions on Computational Science II |
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