Uncertainty in Statistics

Abstract

Uncertainty is the attributed characteristic of life. Understanding the uncertainty fact within predictions and decisions is the way to understand the real fact of life and this is the core of this Thesis. The study of uncertainty theory has been started by determining the states of knowledge which are certainty of knowledge, uncertainty of knowledge and ignorance. As a matter of fact, complete knowledge is an ideal state which impossible to convey. Most of the knowledge lies in the uncertainty area. Then the logically questions raised in this matter are: how does uncertainty arise and how it can be handled? The answers of these questions are given throughout this Thesis. The Thesis contributed some of new results in the area of uncertainty. To start with, new uncertainty space is defined as well as a new uncertainty measure. The new space and measure can be considered as an umbrella covered all uncertainty spaces and measures in the literature. The statistical missing data problem is extensively studied via two perspectives. First, in the sense of rough set. A new approach to handle MCAR, MAR and NMAR, the statistical missing data mechanisms in rough set perspective Moreover, MAR missing values in multi informational systems is developed. The other is the use of similarity relations, a modified similarity relation is proposed and applied. Two of the above results are published and the rest of the results either submitted or prepared for submission.