Introduction

Abstract

Fuzzy measure theory, the subject of this text, is an offspring of classical measure theory. The latter has its roots in metric geometry, which is characterized by assigning numbers to lengths, areas, or volumes. In antiquity, this assignment process, or measurement, was first conceived simply as a comparison with a standard unit. Soon, however, the problem of incommensurables (exemplified by the problem of measuring the length of the diagonal of a square whose sides each measure one unit) revealed that measurement is more complicated than this simple, intuitively suggestive process. It became clear that measurement must inevitably involve infinite sets and infinite processes.