**2. What are fuzzy sets and who uses them?**

Before talking about how to use fuzzy sets for pattern classification,
we must first define what we mean by fuzzy sets. A great source of information
on fuzzy sets and fuzzy logic can be found in a
collection of frequently asked questions and corresponding answers.

*2.1 Fuzzy sets vs. crisp sets*

Crisp sets are the sets that we have used most of our life. In a crisp
set, an element is either a member of the set or not. For example, a jelly
bean belongs in the class of food known as candy. Mashed potatoes do not.

Fuzzy sets, on the other hand, allow elements to be *partially*
in a set. Each element is given a degree of membership in a set. This membership
value can range from 0 (not an element of the set) to 1 (a member of the
set). It is clear that if one only allowed the extreme membership values
of 0 and 1, that this would actually be equivalant to crisp sets. A membership
function is the relationship between the values of an element and its degree
of membership in a set. An example of membership functions are shown in
Figure 2-1. In this example, the sets
(or classes) are numbers that are negative large, negative medium, negative
small, near zero, positive small, positive medium, and positive large.
The value, µ, is the amount of membership in the set.

**Figure 2-1: Membership Functions for the Set of All Numbers (N =
Negative, P = Positive, L = Large, M = Medium, S = Small)**

*2.2 Applications*

Fuzzy sets are appropriate for pattern classification because a given
gesture or pattern may in fact have partial membership in many different
classes. Several companies already have products based on fuzzy pattern
recognition:

1. Hand Writing Recognition: CSK, Hitachi

2. Hand Printed Character Recognition: Sony

3. Voice Recognition: Ricoh, Hitachi