Information Fusion in Signal and Image Processing: Major Probabilistic and Non-Probabilistic Numerical Approaches

Chapter 8

Fuzzy Sets and Possibility Theory

8.1. Introduction and general concepts

As we have seen in the first chapters of this book, imprecisions and uncertainties are inherent to the data handled in the application fields that concern us.

The advantages of fuzzy sets and possibility theory for information processing, particularly in image and vision [KRI 92], fall into the four following categories:

– the ability of fuzzy sets to represent spatial information in images as well as its imprecision, on several levels (local, regional, or global) and in different forms (numerical, symbolic, quantitative, qualitative);

– the possibility of representing very heterogenous information, directly extracted from images or obtained from outside knowledge, such as expert or generic knowledge in a field or about a problem;

– the possibility of generalizing to fuzzy sets operations for manipulating spatial information;

– the various possible semantics;

– the flexibility of the combination operators, which makes it possible to fuse elements of information that are different in nature, in very different situations.

We will particularly insist on this last point.

In this chapter, we will first of all present the basic elements of fuzzy set and possibility theory. Their use in the more specific context of fusion will be discussed later. This theory was introduced by Zadeh and the first article on the subject dates back to 1965 [ZAD 65]. See [DUB 80, KAU 75, ZIM 91] which contain most of the theory. ...