As a branch of mathematics that studies the behavior of random, fuzzy and rough events, uncertainty theory is the generic name of probability theory, credibility theory, and trust theory. The main purpose of this book...
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ISBN:
(数字)9783540399872
As a branch of mathematics that studies the behavior of random, fuzzy and rough events, uncertainty theory is the generic name of probability theory, credibility theory, and trust theory. The main purpose of this book is to provide axiomatic foundations of uncertainty theory. Itwasgenerallybelievedthatthestudyofprobabilitytheorywasstartedby Pascal and Fermat in 1654 when they succeeded in deriving the exact pro- bilities for certain gambling problem. Great progress was achieved when Von Mises initialized the concept of sample space, and ?lled the gape between probability theory and measure theory in 1931. A complete axiomatic fo- dation of probability theory was given by Kolmogoro? in 1933. Since then, probability theory has been developed steadily and has been widely applied in science and engineering. The axiomatic foundation of probability theory will be introduced in Chapter 2. Fuzzy set was initialized by Zadeh via membership function in 1965, and was well developed and applied in a wide variety of real problems. As a fuzzy set of real numbers, the term fuzzy variable was ?rst introduced by Kaufmann in 1975. In order to make a mathematical foundation, Nahmias gave three axioms to de?ne possibility measure in 1978, and Liu gave the fourth axiom to de?ne product possibility measure in 2002. There are three types of measure in the fuzzy world: possibility, necessity, and credibility.
E-commerce has passed through a number of stages in the minds of most readers of the daily press. Initially it was the province of the specialist and considered almost irrelevant to the needs and activities of everyda...
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ISBN:
(数字)9783540400035
ISBN:
(纸本)9783540205180;9783642058110
E-commerce has passed through a number of stages in the minds of most readers of the daily press. Initially it was the province of the specialist and considered almost irrelevant to the needs and activities of everyday life - companies looking for venture capital in this area had little if any chance of obtaining sufficient funds from the rather conservative investors who provided the only source of start-up capital. Then came the dot. com boom -and suddenly e-commerce was the most exciting topic possible! Venture capital was available from every possible source and almost any company with a . com in its name could be assured of instant funding on request. This boom was, inevitably, followed by the dot. com bust and the press wamed that the days of e-commerce were gone, perhaps never to return. This apparently confusing 'stages of growth' model is in reality nothing ofthe sort. E-commerce is simply the logical outcome of combining computers with tele communications networks. The astonishing changes which a global economy has brought with it are reflected in the changes to the way we do business which are increasingly synonymous with e-commerce. Indeed, the term e-commerce itself is coming to mean only the transaction-based component of e-business-'any process that a business organisation conducts over a computer-mediated network' as Thomas Mesenbourg ofthe U. S. Census Bureau said in 1999.
This book provides readers with an introduction to m-polar fuzzy graphs and m-polar fuzzy hypergraphs, covering both theories and applications. A special emphasis is given to m-polar fuzzy graphs at the aim of filling...
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ISBN:
(数字)9783030037512
ISBN:
(纸本)9783030037505
This book provides readers with an introduction to m-polar fuzzy graphs and m-polar fuzzy hypergraphs, covering both theories and applications. A special emphasis is given to m-polar fuzzy graphs at the aim of filling a gap in the literature, namely the absence of a mathematical approach to analyze multi-index, multipolar, and multi-attribute data. The book describes metrics and labeling in m-polar graphs, m-polar fuzzy matroids. It also discusses in detail important applications in decision-making problems and imaging processing. The book is expected to stimulate the curiosity of mathematics, computer scientists, and social scientists alike, and to provide both students and researchers with the necessary knowledge to understand and apply m−polar fuzzy graph theory.
Fuzzy Sets and Their Extensions: Representation, Aggregation and Models Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision Fuzzy sets are now more than 40 years old, and have...
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ISBN:
(数字)9783540737230
ISBN:
(纸本)9783540737223;9783642092909
Fuzzy Sets and Their Extensions: Representation, Aggregation and Models Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision Fuzzy sets are now more than 40 years old, and have come of age. However, the development of fuzzy set theory at the theoretical level, and its successful appli- tions to science and technology have often run in isolation. Only a little part of the theoretical apparatus was effectively used in past applications. The most prominent ones, namely fuzzy rule-based modeling and control engineering, were directly - spired from a seminal paper by Lot? Zadeh in 1973, suggesting how to use expert knowledge for synthetizing control laws, and from the ?rst experiments published by Abe Mamdani. Later in the eighties, when spectacular applications were bl- soming in Japan, fuzzy rule-based systems were systematized and simpli?ed by Michio Sugeno and colleagues, and became a basic approach to non-linear system modeling and control, soon hybridized with neural networks in the nineties. Thus fuzzy systems signi?cantly contributed to the raise of computational intelligence, and a lot of learning techniques for the construction of (supposedly interpretable) fuzzy models from data were developed under the ?ag of softcomputing. Even if this area was quite successful, it is patent that the role, in the success of fuzzy logic, of new fuzzy set-related concepts developed quite at the same time in themathematicalnicheofthefuzzyset communitywaslimited.
This book addresses computer scientists, IT specialists, mathematicians, knowledge engineers and programmers, who are engaged in research and practice of multicriteria decision making. Fuzzy measures, also known as ca...
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ISBN:
(数字)9783030153052
ISBN:
(纸本)9783030153045
This book addresses computer scientists, IT specialists, mathematicians, knowledge engineers and programmers, who are engaged in research and practice of multicriteria decision making. Fuzzy measures, also known as capacities, allow one to combine degrees of preferences, support or fuzzy memberships into one representative value, taking into account interactions between the inputs. The notions of mutual reinforcement or redundancy are modeled explicitly through coefficients of fuzzy measures, and fuzzy integrals, such as the Choquet and Sugeno integrals combine the inputs. Building on previous monographs published by the authors and dealing with different aspects of aggregation, this book especially focuses on the Choquet and Sugeno integrals. It presents a number of new findings concerning computation of fuzzy measures, learning them from data and modeling interactions. The book does not require substantial mathematical background, as all the relevant notions are explained. It is intended as concise, timely and self-contained guide to the use of fuzzy measures in the field of multicriteria decision making.
Fuzziology studies the fuzziness inherent in what we know about ourselves, the sources and nature of our experience, our thoughts and feelings, drives for understanding and urges to create and realise our potential. T...
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ISBN:
(数字)9783790817782
ISBN:
(纸本)9783790815061;9783662003091
Fuzziology studies the fuzziness inherent in what we know about ourselves, the sources and nature of our experience, our thoughts and feelings, drives for understanding and urges to create and realise our potential. This kind of fuzziness is at the core of our existence, at the essence of our humanness. It affects any field of human activity, be it mathematical study of fuzzy equations and fuzzy integrals; engineering design and implementation of fuzzy logic-based methodologies; fuzzy control systems or fuzzy robots. Social fuzziology investigates the role of fuzziness in understanding the dynamic complexity of human existence in the social world. It is a study of the nexus between the complex demands of life -individual and social -and the fuzziness of thinking. Since human evolution over 2 billion years has seen the co-evolution of social complexity with human language and thought, it is likely that the fuzziness of language and thought is especially intimately formed by the demands of social complexity, just as social complexity is sustained by the inherent fuzziness of language and thought. Social fuzziology is not simply one field of application of fuzziology. Given the initial state of the development of fuzziology, social fuzziology needs to develop hand in hand with fuzziology, each helping to advance the other.
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