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 |
Cover
Table of Contents:
- 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