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Author: Maciej Wygralak
Publisher: Springer
ISBN: 3540363823
Category : Mathematics
Languages : en
Pages : 205
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Book Description
Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num bers: the natural numbers. That these complementary aspects of the counting pro cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.
Author: Maciej Wygralak
Publisher: Springer
ISBN: 3540363823
Category : Mathematics
Languages : en
Pages : 205
Get Book Here
Book Description
Counting is one of the basic elementary mathematical activities. It comes with two complementary aspects: to determine the number of elements of a set - and to create an ordering between the objects of counting just by counting them over. For finite sets of objects these two aspects are realized by the same type of num bers: the natural numbers. That these complementary aspects of the counting pro cess may need different kinds of numbers becomes apparent if one extends the process of counting to infinite sets. As general tools to determine numbers of elements the cardinals have been created in set theory, and set theorists have in parallel created the ordinals to count over any set of objects. For both types of numbers it is not only counting they are used for, it is also the strongly related process of calculation - especially addition and, derived from it, multiplication and even exponentiation - which is based upon these numbers. For fuzzy sets the idea of counting, in both aspects, looses its naive foundation: because it is to a large extent founded upon of the idea that there is a clear distinc tion between those objects which have to be counted - and those ones which have to be neglected for the particular counting process.
Author: Przemyslaw Grzegorzewski
Publisher: Springer Science & Business Media
ISBN: 3790817732
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.
Author: Maciej Wygralak
Publisher: Springer
ISBN: 3642346855
Category : Technology & Engineering
Languages : en
Pages : 294
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Book Description
Counting belongs to the most elementary and frequent mental activities of human beings. Its results are a basis for coming to a decision in a lot of situations and dimensions of our life. This book presents a novel approach to the advanced and sophisticated case, called intelligent counting, in which the objects of counting are imprecisely, fuzzily specified. Formally, this collapses to counting in fuzzy sets, interval-valued fuzzy sets or I-fuzzy sets (Atanassov's intuitionistic fuzzy sets). The monograph is the first one showing and emphasizing that the presented methods of intelligent counting are human-consistent: are reflections and formalizations of real, human counting procedures performed under imprecision and, possibly, incompleteness of information. Other applications of intelligent counting in various areas of intelligent systems and decision support will be discussed, too. The whole presentation is self-contained, systematic, and equipped with many examples, figures and tables. Computer and information scientists, researchers, engineers and practitioners, applied mathematicians, and postgraduate students interested in information imprecision are the target readers.
Author: Bernadette Bouchon
Publisher: World Scientific
ISBN: 9812792341
Category : Computers
Languages : en
Pages : 537
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Book Description
Intelligent systems are necessary to handle modern computer-based technologies managing information and knowledge. This book discusses the theories required to help provide solutions to difficult problems in the construction of intelligent systems. Particular attention is paid to situations in which the available information and data may be imprecise, uncertain, incomplete or of a linguistic nature. The main aspects of clustering, classification, summarization, decision making and systems modeling are also addressed. Topics covered in the book include fundamental issues in uncertainty, the rapidly emerging discipline of information aggregation, neural networks, Bayesian networks and other network methods, as well as logic-based systems.
Author: Miguel Concepcion Lopez-Diaz
Publisher: Springer Science & Business Media
ISBN: 3540444653
Category : Mathematics
Languages : en
Pages : 769
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Book Description
The analysis of experimental data resulting from some underlying random process is a fundamental part of most scientific research. Probability Theory and Statistics have been developed as flexible tools for this analyis, and have been applied successfully in various fields such as Biology, Economics, Engineering, Medicine or Psychology. However, traditional techniques in Probability and Statistics were devised to model only a singe source of uncertainty, namely randomness. In many real-life problems randomness arises in conjunction with other sources, making the development of additional "softening" approaches essential. This book is a collection of papers presented at the 2nd International Conference on Soft Methods in Probability and Statistics (SMPS’2004) held in Oviedo, providing a comprehensive overview of the innovative new research taking place within this emerging field.
Author: Salvatore Greco
Publisher: Springer
ISBN: 3642317154
Category : Computers
Languages : en
Pages : 615
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Book Description
These four volumes (CCIS 297, 298, 299, 300) constitute the proceedings of the 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, held in Catania, Italy, in July 2012. The 258 revised full papers presented together with six invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy machine learning and on-line modeling; computing with words and decision making; soft computing in computer vision; rough sets and complex data analysis: theory and applications; intelligent databases and information system; information fusion systems; philosophical and methodological aspects of soft computing; basic issues in rough sets; 40th anniversary of the measures of fuziness; SPS11 uncertainty in profiling systems and applications; handling uncertainty with copulas; formal methods to deal with uncertainty of many-valued events; linguistic summarization and description of data; fuzzy implications: theory and applications; sensing and data mining for teaching and learning; theory and applications of intuitionistic fuzzy sets; approximate aspects of data mining and database analytics; fuzzy numbers and their applications; information processing and management of uncertainty in knowledge-based systems; aggregation functions; imprecise probabilities; probabilistic graphical models with imprecision: theory and applications; belief function theory: basics and/or applications; fuzzy uncertainty in economics and business; new trends in De Finetti's approach; fuzzy measures and integrals; multicriteria decision making; uncertainty in privacy and security; uncertainty in the spirit of Pietro Benvenuti; coopetition; game theory; probabilistic approach.
Author: Engelbert Mephu Nguifo
Publisher: Springer Science & Business Media
ISBN: 3540789200
Category : Computers
Languages : en
Pages : 292
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Book Description
As the refereed proceedings of the Fourth International Conference on Concept Lattices and their Applications, CLA 2006, these 18 revised full papers, together with 3 invited contributions, presented were carefully reviewed and selected from 41 submissions.
Author: Cecilio Angulo
Publisher: IOS Press
ISBN: 1586037986
Category : Computers
Languages : en
Pages : 452
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Book Description
Contains papers which were presented at the 10th anniversary of the International Conference of the ACIA (CCIA'07) in Sant Julia de Loria (Andorra), October 25-26th, 2007. This book is intended for those computer scientists or engineers who are interested in artificial intelligence."
Author: Djamel A. Zighed
Publisher: Springer
ISBN: 3540453725
Category : Computers
Languages : en
Pages : 717
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Book Description
This book constitutes the refereed proceedings of the 4th European Conference on Principles and Practice of Knowledge Discovery in Databases, PKDD 2000, held in Lyon, France in September 2000. The 86 revised papers included in the book correspond to the 29 oral presentations and 57 posters presented at the conference. They were carefully reviewed and selected from 147 submissions. The book offers topical sections on new directions, rules and trees, databases and reward-based learning, classification, association rules and exceptions, instance-based discovery, clustering, and time series analysis.
Author: Rajiv Khosla
Publisher: Springer
ISBN: 3540319832
Category : Computers
Languages : en
Pages : 1396
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Book Description
Dear delegates,friendsand membersofthe growingKES professionalcommunity,w- come to the proceedings of the 9th International Conference on Knowledge-Based and IntelligentInformationandEngineeringSystemshostedbyLa TrobeUniversityin M- bourne Australia. The KES conference series has been established for almost a decade, and it cont- ues each year to attract participants from all geographical areas of the world, including Europe, the Americas, Australasia and the Paci?c Rim. The KES conferences cover a wide range of intelligent systems topics. The broad focus of the conference series is the theory and applications of intelligent systems. From a pure research ?eld, intel- gent systems have advanced to the point where their abilities have been incorporated into many business and engineering application areas. KES 2005 provided a valuable mechanism for delegates to obtain an extensive view of the latest research into a range of intelligent-systems algorithms, tools and techniques. The conference also gave de- gates the chance to come into contact with those applying intelligent systems in diverse commercial areas. The combination of theory and practice represented a unique opp- tunity to gain an appreciation of the full spectrum of leading-edge intelligent-systems activity. The papers for KES 2005 were either submitted to invited sessions, chaired and organized by respected experts in their ?elds, or to a general session, managed by an extensive International Program Committee, or to the Intelligent Information Hiding and Multimedia Signal Processing (IIHMSP) Workshop, managed by an International Workshop Technical Committee.
