This monograph introduces elementary fuzzy statistics based on crisp (non-fuzzy) data. In the introductory chapters the book presents a very readable survey of fuzzy sets including fuzzy arithmetic and fuzzy functions. The book develops fuzzy estimation and demonstrates the construction of fuzzy estimators for various important and special cases of variance, mean and distribution functions. It is shown how to use fuzzy estimators in hypothesis testing and regression, which leads to a comprehensive presentation of fuzzy hypothesis testing and fuzzy regression as well as fuzzy prediction.

Klappentext

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.

   Inhalt

   Fuzzy Sets.- Estimate ?, Variance Known.- Estimate ?, Variance Unknown.- Estimate p, Binomial Population.- Estimate ?2 from a Normal Population.- Estimate µ 1 - µ 2, Variances Known.- Estimate ? 1 - ? 2, Variances Unknown.- Estimate d =? 1 - ? 2, Matched Pairs.- Estimate p 1 - p 2, Binomial Populations.- Estimate ? 1 2 /? 2 2 , Normal Populations.- Tests on µ, Variance Known.- Tests on µ, Variance Unknown.- Tests on p for a Binomial Population.- Tests on ? 2, Normal Population.- Tests ? 1 verses ? 2, Variances Known.- Test ? 1 verses ? 2, Variances Unknown.- Test p 1 = p 2, Binomial Populations.- Test d = µ 1 - µ 2 , Matched Pairs.- Test ? 1 2 verses ? 2 2 , 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.