Fuzzy subsets were introduced in 1965 by L.A. Zadeh [Zadeh, 1965]. The purpose of the fuzzy set concept [Bouchon-Meunier, 1995] is to authorize an element to belong to a class more or less strongly . For example, a man of a given size:

• does not belong at all to the class `` tall '' if he measures 1.50 meters,
• he belongs to it completely if he measures 1.80 meters and,
• as his size approaches 1.80 meters, his membership of the class `` tall '' becomes strong.

This notion allows us to deal with:

• classes with poorly defined boundaries (such that `` young '' or `` far '');
• intermediate situations between the whole and nothing (`` almost true '');
• the progressive transition from one property to another (transition from `` warm '' to `` hot '' as the temperature changes;
• the use of approximate values (`` about 12 years '').

It avoids the arbitrary use of rigid limits to classes. In the previous example, it would be absurd to consider that a man of 1.78 meters is tall, but that another of 1.775 meters is absolutely not tall.

The concept of fuzzy set softens the classical concept of subset.

• Definitions
• Definition of a Fuzzy (Sub)Set
• Fuzzy Subset Features
• Example 1
• Example 2