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.
