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.
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.
Inhaltsverzeichnis
Regular Papers.- 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.
