"Decision Systems and Non-shastic Randomness" is the first systematic presentation and mathematical formalization (including existence theorems) of the statistical regularities of non-shastic randomness. The results presented in this book extend the capabilities of probability theory by providing mathematical techniques that allow for the description of uncertain events that do not fit standard shastic models. The book demonstrates how non-shastic regularities can be incorporated into decision theory and information theory, offering an alternative to the subjective probability approach to uncertainty and the unified approach to the measurement of information. This book is intended for statisticians, mathematicians, engineers, economists or other researchers interested in non-shastic modeling and decision theory.