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Fuzzy Statistics : Studies in Fuzziness and Soft Computing - James J. Buckley

Fuzzy Statistics

Studies in Fuzziness and Soft Computing

Hardcover

Published: 5th April 2004
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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.

Introduction
Fuzzy Sets
Estimate , Variance Known
Estimate , Variance Unknown
Estimate p, Binomial Population
Estimate sigma[2] from a Normal Population
Estimate 1 - 2, Variances Known
Estimate 1 - 2, Variances Unknown
Estimate d = 1 - 2, Matched Pairs
Estimate p1 - p2, Binomial Populations
Estimate sigma sub one squared/sigma sub two squared, Normal Populations
Tests on , Variance Known
Tests on , Variance Unknown
Tests on p for a Binomial Population
Tests on sigma2, Normal Population
Tests 1 vs. 2, Variances Known
Test 1 vs. 2, Variances Unknown
Test p1 = p2, Binomial Populations
Test d = 1 - 2, Matched Pairs
Test sigma sub one squared vs. sigma sub two squared, Normal Populations
Fuzzy Correlation
Estimation in Simple Linear Regression
Fuzzy Prediction in Linear Regression
Hypothesis Testing in Regression
Estimation in Multiple Regression
Fuzzy Prediction in Regression
Hypothesis Testing in Regression
Summary and Questions
Maple Commands
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540210849
ISBN-10: 3540210849
Series: Studies in Fuzziness and Soft Computing
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 168
Published: 5th April 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.27
Weight (kg): 0.96