1.1 Introduction This book is written in five major divisions. The first part is the introduc tory chapters consisting of Chapters 1-3. In part two, Chapters 4-10, we use fuzzy probabilities to model a fuzzy que...
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ISBN:
(数字)9783540364269
ISBN:
(纸本)9783540004738;9783642055966
1.1 Introduction This book is written in five major divisions. The first part is the introduc tory chapters consisting of Chapters 1-3. In part two, Chapters 4-10, we use fuzzy probabilities to model a fuzzy queuing system . We switch to employ ing fuzzy arrival rates and fuzzy service rates to model the fuzzy queuing system in part three in Chapters 11 and 12. Optimization models comprise part four in Chapters 13-17. The final part has a brief summary and sug gestions for future research in Chapter 18, and a summary of our numerical methods for calculating fuzzy probabilities, values of objective functions in fuzzy optimization, etc., is in Chapter 19. First we need to be familiar with fuzzy sets. All you need to know about fuzzy sets for this book comprises Chapter 2. Two other items relating to fuzzy sets, needed in Chapters 13-17, are also in Chapter 2: (1) how we plan to handle the maximum/minimum of a fuzzy set; and (2) how we will rank a finite collection of fuzzy numbers from smallest to largest.
1. 1 Introduction This book is written in four major divisions. The first part is the introductory chapters consisting of Chapters 1 and 2. In part two, Chapters 3-11, we develop fuzzy estimation. For example, in Chap...
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ISBN:
(数字)9783540399193
ISBN:
(纸本)9783540210849;9783642059247
1. 1 Introduction This book is written in four major divisions. The first part is the introductory chapters consisting of Chapters 1 and 2. In part two, Chapters 3-11, we develop fuzzy estimation. For example, in Chapter 3 we construct a fuzzy estimator for the mean of a normal distribution assuming the variance is known. More details on fuzzy estimation are in Chapter 3 and then after Chapter 3, Chapters 4-11 can be read independently. Part three, Chapters 12- 20, are on fuzzy hypothesis testing. For example, in Chapter 12 we consider the test Ho : /1 = /10 verses HI : /1 f=- /10 where /1 is the mean of a normal distribution with known variance, but we use a fuzzy number (from Chapter 3) estimator of /1 in the test statistic. More details on fuzzy hypothesis testing are in Chapter 12 and then after Chapter 12 Chapters 13-20 may be read independently. Part four, Chapters 21-27, are on fuzzy regression and fuzzy prediction. We start with fuzzy correlation in Chapter 21. Simple linear regression is the topic in Chapters 22-24 and Chapters 25-27 concentrate on multiple linear regression. Part two (fuzzy estimation) is used in Chapters 22 and 25; and part 3 (fuzzy hypothesis testing) is employed in Chapters 24 and 27. Fuzzy prediction is contained in Chapters 23 and 26. A most important part of our models in fuzzy statistics is that we always start with a random sample producing crisp (non-fuzzy) data.
Science has made great progress in the twentieth century, with the establishment of proper disciplines in the fields of physics, computer science, molecular biology, and many others. At the same time, there have also ...
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ISBN:
(数字)9783540400462
ISBN:
(纸本)9783540205845;9783642058202
Science has made great progress in the twentieth century, with the establishment of proper disciplines in the fields of physics, computer science, molecular biology, and many others. At the same time, there have also emerged many engineering ideas that are interdisciplinary in nature, beyond the realm of such orthodox disciplines. These in clude, for example, artificial intelligence, fuzzy logic, artificial neural networks, evolutional computation, data mining, and so on. In or der to generate new technology that is truly human-friendly in the twenty-first century, integration of various methods beyond specific disciplines is required. softcomputing is a key concept for the creation of such human friendly technology in our modern information society. Professor Rutkowski is a pioneer in this field, having devoted himself for many years to publishing a large variety of original work. The present vol ume, based mostly on his own work, is a milestone in the devel opment of softcomputing, integrating various disciplines from the fields of information science and engineering. The book consists of three parts, the first of which is devoted to probabilistic neural net works. Neural excitation is stochastic, so it is natural to investi gate the Bayesian properties of connectionist structures developed by Professor Rutkowski. This new approach has proven to be par ticularly useful for handling regression and classification problems vi Preface in time-varying environments. Throughout this book, major themes are selected from theoretical subjects that are tightly connected with challenging applications.
It was generally believed that the study of probability theory was started by Pascal and Fermat in 1654 when they succeeded in deriving the exact probabilitiesforcertaingamblingproblem. Greatprogresswasachievedwhen Vo...
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ISBN:
(数字)9783540731658
ISBN:
(纸本)9783642092176
It was generally believed that the study of probability theory was started by Pascal and Fermat in 1654 when they succeeded in deriving the exact probabilitiesforcertaingamblingproblem. Greatprogresswasachievedwhen VonMisesinitializedtheconceptofsamplespace, and?lledthegapebetween probability theory and measure theory in 1931. An axiomatic foundation of probabilitytheorywasgivenbyKolmogoro?inhisFoundationsofProbability Theory of 1933. Since then, probability theory has been developed steadily and has been widely applied in science and engineering. Probability theory will be introduced in Chapter 2. Fuzzy set was initiated by Zadeh via membership function in 1965, and was well developed and applied in a wide variety of real problems. In order to measure a fuzzy event, Zadeh proposed the concept of possibility measure in 1978. Although possibility measure has been widely used, it has no se- duality property. However, a self-dual measure is absolutely needed in both theory and practice. In order to de?ne a self-dual measure, Liu and Liu gave the concept of credibility measure in 2002. Credibility theory is a branch of mathematics that studies the behavior of fuzzy phenomena. An axiomatic foundation of credibility theory was given by Liu in his Uncertainty Theory of 2004. Chapter 3 will provide the credibility theory. Sometimes, fuzziness and randomness simultaneously appear in a system.
Applications of softcomputing have recently increased and methodological development has been strong. The book is a collection of new interesting industrial applications introduced by several research groups and indu...
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ISBN:
(数字)9783790818222
ISBN:
(纸本)9783790813883;9783790824889
Applications of softcomputing have recently increased and methodological development has been strong. The book is a collection of new interesting industrial applications introduced by several research groups and industrial partners. It describes the principles and results of industrial applications of softcomputing methods and introduces new possibilities to gain technical and economic benefits by using this methodology. The book shows how fuzzy logic and neural networks have been used in the Finnish paper and metallurgical industries putting emphasis on processes, applications and technical and economic results.
Intelligent agents are one of the most promising business tools in our information rich world. An intelligent agent consists of a software system capable of performing intelligent tasks within a dynamic and unpredicta...
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ISBN:
(数字)9783790817867
ISBN:
(纸本)9783790814699;9783790825107
Intelligent agents are one of the most promising business tools in our information rich world. An intelligent agent consists of a software system capable of performing intelligent tasks within a dynamic and unpredictable environment. They can be characterised by various attributes including: autonomous, adaptive, collaborative, communicative, mobile, and reactive. Many problems are not well defined and the information needed to make decisions is not available. These problems are not easy to solve using conventional computing approaches. Here, the intelligent agent paradigm may play a major role in helping to solve these problems. This book, written for application researchers, covers a broad selection of research results that demonstrate, in an authoritative and clear manner, the applications of agents within our information society.
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