Cardinalities Of Fuzzy Sets
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Cardinalities Of Fuzzy Sets
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Author : Maciej Wygralak
language : en
Publisher: Springer
Release Date : 2012-12-06
Cardinalities Of Fuzzy Sets written by Maciej Wygralak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Cardinalities Of Fuzzy Sets
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Author : Maciej Wygralak
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-03-11
Cardinalities Of Fuzzy Sets written by Maciej Wygralak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-11 with Mathematics categories.
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.
Theoretical Advances And Applications Of Fuzzy Logic And Soft Computing
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Author : Oscar Castillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-10
Theoretical Advances And Applications Of Fuzzy Logic And Soft Computing written by Oscar Castillo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-10 with Technology & Engineering categories.
This book comprises a selection of papers on theoretical advances and applications of fuzzy logic and soft computing from the IFSA 2007 World Congress, held in Cancun, Mexico, June 2007. These papers constitute an important contribution to the theory and applications of fuzzy logic and soft computing methodologies.
Soft Methods In Probability Statistics And Data Analysis
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Author : Przemyslaw Grzegorzewski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Soft Methods In Probability Statistics And Data Analysis written by Przemyslaw Grzegorzewski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
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.
Fuzzy Logic And Soft Computing
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Author : Bernadette Bouchon-meunier
language : en
Publisher: World Scientific
Release Date : 1995-09-15
Fuzzy Logic And Soft Computing written by Bernadette Bouchon-meunier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-15 with Computers categories.
Soft computing is a new, emerging discipline rooted in a group of technologies that aim to exploit the tolerance for imprecision and uncertainty in achieving solutions to complex problems. The principal components of soft computing are fuzzy logic, neurocomputing, genetic algorithms and probabilistic reasoning.This volume is a collection of up-to-date articles giving a snapshot of the current state of the field. It covers the whole expanse, from theoretical foundations to applications. The contributors are among the world leaders in the field.
Fuzzy Sets And Applications
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Author : Lotfi Asker Zadeh
language : en
Publisher: Wiley-Interscience
Release Date : 1987-05-08
Fuzzy Sets And Applications written by Lotfi Asker Zadeh and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-05-08 with Computers categories.
This volume contains the most significant papers written by L. A. Zadeh, who in 1965 introduced the concept of a fuzzy set. Fuzzy set theory has become the foundation for the development of the fields of artificial intelligence and expert systems, especially in the applications of knowledge-based systems. As such, Zadeh's work has influenced researchers around the world. Zadeh has cooperated with editors in choosing the papers presented here, and the editors have provided an introduction for each paper. Topics covered include probability measures of fuzzy events, similarity relations and fuzzy orderings, a fuzzy-algorithmic approach to the definition of complex or imprecise concepts, and much more.
Information Processing And Management Of Uncertainty In Knowledge Based Systems
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Author : Eyke Hüllermeier
language : en
Publisher: Springer
Release Date : 2010-06-29
Information Processing And Management Of Uncertainty In Knowledge Based Systems written by Eyke Hüllermeier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-29 with Computers categories.
The International Conference on Information Processing and Management of - certainty in Knowledge-Based Systems, IPMU, is organized every two years with the aim of bringing together scientists working on methods for the management of uncertainty and aggregation of information in intelligent systems. Since 1986, this conference has been providing a forum for the exchange of ideas between th theoreticians and practitioners working in these areas and related ?elds. The 13 IPMU conference took place in Dortmund, Germany, June 28–July 2, 2010. This volume contains 79 papers selected through a rigorous reviewing process. The contributions re?ect the richness of research on topics within the scope of the conference and represent several important developments, speci?cally focused on theoretical foundations and methods for information processing and management of uncertainty in knowledge-based systems. We were delighted that Melanie Mitchell (Portland State University, USA), Nihkil R. Pal (Indian Statistical Institute), Bernhard Sch ̈ olkopf (Max Planck I- titute for Biological Cybernetics, Tubing ̈ en, Germany) and Wolfgang Wahlster (German Research Center for Arti?cial Intelligence, Saarbruc ̈ ken) accepted our invitations to present keynote lectures. Jim Bezdek received the Kamp ́ede F ́ eriet Award, granted every two years on the occasion of the IPMU conference, in view of his eminent research contributions to the handling of uncertainty in clustering, data analysis and pattern recognition.
Advances In Computational Intelligence Part Ii
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Author : Salvatore Greco
language : en
Publisher: Springer
Release Date : 2012-07-20
Advances In Computational Intelligence Part Ii written by Salvatore Greco and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-20 with Computers categories.
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.
Intelligent Counting Under Information Imprecision
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Author : Maciej Wygralak
language : en
Publisher: Springer
Release Date : 2013-08-23
Intelligent Counting Under Information Imprecision written by Maciej Wygralak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-23 with Technology & Engineering categories.
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.
Artificial Intelligence And Soft Computing Icaisc 2008
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Author : Leszek Rutkowski
language : en
Publisher: Springer
Release Date : 2008-06-19
Artificial Intelligence And Soft Computing Icaisc 2008 written by Leszek Rutkowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-19 with Computers categories.
This book constitutes the refereed proceedings of the 9th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2008, held in Zakopane, Poland, in June 2008. The 116 revised contributed papers presented were carefully reviewed and selected from 320 submissions. The papers are organized in topical sections on neural networks and their applications, fuzzy systems and their applications, evolutionary algorithms and their applications, classification, rule discovery and clustering, image analysis, speech and robotics, bioinformatics and medical applications, various problems of artificial intelligence, and agent systems.