Introduction

Abstract

In this monograph, problems resulting from two types of uncertainty — randomness and vagueness — are treated. Randomness involves only uncertainties in the outcomes of an experiment; vagueness, on the other hand, involves uncertainties in the meaning of the data. Examples of randomness can be found in any well-defined random experiment such as tossing a coin, observing queues, and recording observed signals. Examples of vagueness include experiments involving linguistic data, which for the purpose of information processing have to be modeled with greater care. A typical example of the occurrence of vague data is to be seen in knowledge-based systems, in which the combined knowledge of a group of experts is often vague.