Cardinalities of Fuzzy Sets PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Cardinalities of Fuzzy Sets PDF full book. Access full book title Cardinalities of Fuzzy Sets by Maciej Wygralak. Download full books in PDF and EPUB format.
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: 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: M. Wygralak
Publisher: Springer
ISBN: 0585275238
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
In recent years, an impetuous development of new, unconventional theories, methods, techniques and technologies in computer and information sciences, systems analysis, decision-making and control, expert systems, data modelling, engineering, etc. , resulted in a considerable increase of interest in adequate mathematical description and analysis of objects, phenomena, and processes which are vague or imprecise by their very nature. Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their (too) categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc. This is why one replaces classical logic by various types of many-valued logics and, on the other hand, more general notions are introduced instead of or beside that of a set. Let us mention, for instance, fuzzy sets and derivative concepts, flou sets and twofold fuzzy sets, which have been created for different purposes as well as using distinct formal and informal motivations. A kind of numerical information concerning of 'how many' elements those objects are composed seems to be one of the simplest and more important types of information about them. To get it, one needs a suitable notion of cardinality and, moreover, a possibility to calculate with such cardinalities. Unfortunately, neither fuzzy sets nor the other nonclassical concepts have been equipped with a satisfactory (nonclassical) cardinality theory.
Author: Oscar Castillo
Publisher: Springer Science & Business Media
ISBN: 3540724346
Category : Technology & Engineering
Languages : en
Pages : 626
Get Book Here
Book Description
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.
Author: Bhargava A.K.
Publisher: S. Chand Publishing
ISBN: 8121941946
Category : Science
Languages : en
Pages : 400
Get Book Here
Book Description
Classical Sets Fuzzy Relation Equations Basic Concepts On Fuzzy Sets Possibility Theory Fuzzy Sets Versus Crisp Sets Fuzzy Logic Operations On Fuzzy Sets Uncertainty-Based Information Interval Arithmetic Approximate Reasoning Fuzzy Numbers And Fuzzy Arithmetic Fuzzy Control And Fuzzy Expert Systems Fuzzy Relations Fuzzy Decision Making Index
Author: Didier J. Dubois
Publisher: Morgan Kaufmann
ISBN: 1483214508
Category : Computers
Languages : en
Pages : 929
Get Book Here
Book Description
Readings in Fuzzy Sets for Intelligent Systems is a collection of readings that explore the main facets of fuzzy sets and possibility theory and their use in intelligent systems. Basic notions in fuzzy set theory are discussed, along with fuzzy control and approximate reasoning. Uncertainty and informativeness, information processing, and membership, cognition, neural networks, and learning are also considered. Comprised of eight chapters, this book begins with a historical background on fuzzy sets and possibility theory, citing some forerunners who discussed ideas or formal definitions very close to the basic notions introduced by Lotfi Zadeh (1978). The reader is then introduced to fundamental concepts in fuzzy set theory, including symmetric summation and the setting of fuzzy logic; uncertainty and informativeness; and fuzzy control. Subsequent chapters deal with approximate reasoning; information processing; decision and management sciences; and membership, cognition, neural networks, and learning. Numerical methods for fuzzy clustering are described, and adaptive inference in fuzzy knowledge networks is analyzed. This monograph will be of interest to both students and practitioners in the fields of computer science, information science, applied mathematics, and artificial intelligence.
Author: Bernadette Bouchon-meunier
Publisher: World Scientific
ISBN: 9814500089
Category : Computers
Languages : en
Pages : 509
Get Book Here
Book Description
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.
Author: Rainer Hampel
Publisher: Springer Science & Business Media
ISBN: 3790818410
Category : Technology & Engineering
Languages : en
Pages : 413
Get Book Here
Book Description
The present edited volume is of special importance, and for various reasons. First of all, it is one of the most comprehensive and multifaceted coverage of broadly per ceived fuzzy control in the literature. The editors have succeeded to collect papers from leading scholars and researchers on various subjects related to the topic of the volume. What is relevant and original is that - as opposed to so many volumes on fuzzy control published by virtually all major publishing houses that are strongly technically oriented and covering a narrow spectrum of issues relevant to fuzzy con trol itself - the editors have adopted a more general and far sighted approach. Basically, the perspective assumed in the volume is that though fuzzy control has reached such a level of maturity and implementability that it has become a part of in dustrial practice, science and academic research still have a relevant role to play in this area. One should however take into account that by their very nature, the role of science and academic research is very peculiar and going beyond straightforward ap plications, ad hoc solutions, "quick and dirty" tools and techniques, etc. that are usu ally effective and efficient for solving practical problems. This does not mean that as pects of practical implementations should not be accounted for by scholars and re searchers.
Author: Przemyslaw Grzegorzewski
Publisher: Springer Science & Business Media
ISBN: 3790817732
Category : Mathematics
Languages : en
Pages : 376
Get Book Here
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: Taner Bilgic
Publisher: Springer
ISBN: 3540449671
Category : Technology & Engineering
Languages : en
Pages : 751
Get Book Here
Book Description
The refereed proceedings of the 10th International Fuzzy Systems Association World Congress, IFSA 2003, held in June/July 2003 in Istanbul, Turkey. The 84 papers presented together with 5 invited papers were carefully reviewed and selected form 318 submissions. The papers address all current issues in the area and present the state of the art in fuzzy sets, fuzzy systems, and fuzzy logic and their applications in a broad variety of fields. The papers are divided in four parts on mathematical issues, methodological issues, application areas, and cross-disciplinary issues.
Author: Alireza Sadeghian
Publisher: Springer
ISBN: 1461434424
Category : Technology & Engineering
Languages : en
Pages : 266
Get Book Here
Book Description
Frontiers of Higher Order Fuzzy Sets, provides a unified representation theorem for higher order fuzzy sets. The book elaborates on the concept of gradual elements and their integration with the higher order fuzzy sets. This book also is devoted to the introduction of new frameworks based on general T2FSs, IT2FSs, Gradual elements, Shadowed sets and rough sets. Such new frameworks will provide more capable frameworks for real applications. Applications of higher order fuzzy sets in various fields will be discussed. In particular, the properties and characteristics of the new proposed frameworks would be studied. Such frameworks that are the result of the integration of general T2FSs, IT2FSs, gradual elements, shadowed sets and rough sets will be shown to be suitable to be applied in the fields of bioinformatics, business, management, ambient intelligence, medicine, cloud computing and smart grids.
