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Mathematics of Uncertainty
"Mathematics of Uncertainty" provides the basic ideas and foundations of uncertainty, covering the fields of mathematics in which uncertainty, variability, imprecision and fuzziness of data are of importance. This introductory book describes the basic ideas of the mathematical fields of uncertainty from simple interpolation to wavelets, from error propagation to fuzzy sets and neural networks. The book presents the treatment of problems of interpolation and approximation, as well as observation fuzziness which can essentially influence the preciseness and reliability of statements on functional relationships. The notions of randomness and probability are examined as a model for the variability of observation and measurement results. Besides these basic ideas the book also presents methods of qualitative data analysis such as cluster analysis and classification, and of evaluation of functional relationships such as regression analysis and quantitative fuzzy data analysis.
Space, Structure and Randomness
Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. Th...
Fuzzy Data Analysis
Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common. In Fuzzy Data Analysis the authors collect their recent results providing the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge bases for an evaluation of functional relationship, e.g. in order to specify diagnostic or control systems. The modelling presented uses ideas from fuzzy set theory and the suggested methods solve problems usually tackled by data analysis if the data are real numbers. Fuzzy Data Analysis is self-contained and is addressed to mathematicians oriented towards applications and to practitioners in any field of application who have some background in mathematics and statistics.
Soft Computing in Ontologies and Semantic Web
This book covers in a great depth the fast growing topic of tools, techniques and applications of soft computing (e.g., fuzzy logic, genetic algorithms, neural networks, rough sets, Bayesian networks, and other probabilistic techniques) in the ontologies and the Semantic Web. The author shows how components of the Semantic Web (like the RDF, Description Logics, ontologies) can be covered with a soft computing methodology.
Fuzzy Approach to Reasoning and Decision-Making
Selected Papers of the International Symposium held at Bechyne, June 25-29, 1990
Flexible Databases Supporting Imprecision and Uncertainty
This volume offers the advice of selected expert contributors on the application of heterogeneous methods for managing uncertainty and imprecision in databases. It contains both survey chapters on classic topics such as "flexible querying in databases", and up to date information on "database models to represent imperfect data". Further, it includes specific contributions on uncertainty management in database integration, and in representing and querying semistructured and spatial data.
Power Algebras over Semirings
This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimizati...
Fuzzy Chaotic Systems
This book presents the fundamental concepts of fuzzy logic and fuzzy control, chaos theory and chaos control. It also provides a definition of chaos on the metric space of fuzzy sets. The book raises many questions and generates a great potential to attract more attention to combine fuzzy systems with chaos theory. In this way it contains important seeds for future scientific research and engineering applications.
Soft Computing in Web Information Retrieval
This book presents recent studies on the application of Soft Computing techniques in information access on the World Wide Web. The book is divided in four parts reflecting the areas of research of the presented works such as Document Classification, Semantic Web, Web Information Retrieval and Web Applications. The text demonstrates that Web Information Retrieval is a stimulating area of research where Soft Computing technologies can be applied satisfactorily.
Fuzzy Database Modeling of Imprecise and Uncertain Engineering Information
Computer-based information technologies have been extensively used to help industries manage their processes and information systems hereby - come their nervous center. More specially, databases are designed to s- port the data storage, processing, and retrieval activities related to data management in information systems. Database management systems p- vide efficient task support and database systems are the key to impleme- ing industrial data management. Industrial data management requires da- base technique support. Industrial applications, however, are typically data and knowledge intensive applications and have some unique character- tics that makes their management difficult. Besides, ...
