Fuzzy Probabilities
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| Author | : James J. Buckley |
| Publisher | : Physica |
| Total Pages | : 168 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642867863 |
In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.
| Author | : James J. Buckley |
| Publisher | : Springer |
| Total Pages | : 262 |
| Release | : 2008-09-12 |
| Genre | : Computers |
| ISBN | : 3540331905 |
This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.
| Author | : James J. Buckley |
| Publisher | : Springer |
| Total Pages | : 166 |
| Release | : 2013-11-11 |
| Genre | : Technology & Engineering |
| ISBN | : 3540399194 |
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.
| Author | : Timothy J. Ross |
| Publisher | : SIAM |
| Total Pages | : 424 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898715253 |
Shows both the shortcomings and benefits of each technique, and even demonstrates useful combinations of the two.
| Author | : Gholamreza Hesamian |
| Publisher | : CRC Press |
| Total Pages | : 288 |
| Release | : 2022 |
| Genre | : Mathematics |
| ISBN | : 9781003248644 |
This book presents the most commonly used techniques for the most statistical inferences based on fuzzy data. It brings together many of the main ideas used in statistical inferences in one place, based on fuzzy information including fuzzy data. This book covers a much wider range of topics than a typical introductory text on fuzzy statistics. It includes common topics like elementary probability, descriptive statistics, hypothesis tests, one-way ANOVA, control-charts, reliability systems and regression models The reader is assumed to know calculus and a little fuzzy set theory. The conventional knowledge of probability and statistics is required. Key Features: Includes example in Mathematica and MATLAB. Contains theoretical and applied exercises for each section. Presents various popular methods for analyzing fuzzy data. The book is suitable for students and researchers in statistics, social science, engineering, and economics, and it can be used at graduate and P.h.D level. Gholamreza Hesamian is Associate Professor of Statistics at Payame Noor University. His research areas include decision theory, probability theory, fuzzy mathematics, and statistics.
| Author | : Kofi Kissi Dompere |
| Publisher | : Springer |
| Total Pages | : 311 |
| Release | : 2009-07-28 |
| Genre | : Mathematics |
| ISBN | : 3540880879 |
We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The “degree” of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.
| Author | : Madan L. Puri |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 456 |
| Release | : 2018-11-05 |
| Genre | : Mathematics |
| ISBN | : 3110942003 |
No detailed description available for "Asymptotics in Statistics and Probability".
| Author | : Madan M. Gupta |
| Publisher | : North-Holland |
| Total Pages | : 772 |
| Release | : 1979 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 143 |
| Release | : 2017-10-01 |
| Genre | : Mathematics |
| ISBN | : |
We introduce for the first time the concept of plithogeny in philosophy and, as a derivative, the concepts of plithogenic set / logic / probability / statistics in mathematics and engineering – and the degrees of contradiction (dissimilarity) between the attributes’ values that contribute to a more accurate construction of plithogenic aggregation operators and to the plithogenic relationship of inclusion (partial ordering).
| Author | : Hung T. Nguyen |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2006-02-28 |
| Genre | : Mathematics |
| ISBN | : 3540316973 |
This book presents basic aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The book aims at motivating statisticians to examine fuzzy statistics to enlarge the domain of applicability of statistics in general.
