Research for Probability Theory

Many uncertainties associated with exercise reconstruction may be modeled as random processes; however, many other uncertainties in exercise reconstruction are not due to random processes but are due to imprecise or ambiguous information. Fuzzy sets and possibility theory have been developed over the last 20 years for the analysis of nonrandom, imprecise events. This research memorandum explores the possible use of fuzzy-set techniques in exercise reconstruction. Fuzzy sets are defined and examples are given.

A simple procedure to approximate a confidence interval for the parameter n in a binomial distribution is presented in this research memorandum. A simulation procedure to verify the coverage of confidence intervals is presented in appendix A. An interactive computer program is included in appendix B. The program is written in the FORTRAN language, which is readily available in most computing environments. Tables with 90 percent and 95 percent confidence coefficients are included in appendix C.

Within a few years the Department of Defense may begin administering the Armed Services Vocational Aptitude Battery (ASVAB) using Computerized Adaptive Testing (CAT). Each test item is characterized by an Item Response Curve (IRC), which describes how the probability of correctly answering the item increases with ability. One important question in the CAT project is whether the IRCs are the same in paper-pencil and CAT administrations. This paper examines this issue.

In World War II, the phrase 'operations research' has come to describe the scientific, quantitative study of operations of war. This report is a first attempt to describe some of the methods which have proved most valuable in the study of warfare, and to indicate possible fruitful lines for further development, military and nonmilitary. The first chapter outlines the scope and methods of the subject. The second chapter discusses the relevant portions of the theory of probability, which is the field of mathematics most useful for this work. The rest of the chapters discuss techniques which have been particularly useful, with illustrations picked from work done in the recent war.