ABSTRACT

The aim of this chapter is to consider new classes of validity functionals based on various philosophies. An important class is that of uniform data validity functionals. Geometric validity functionals that intend to reflect the actual structure of the data set are considered. These geometric functionals also relate to the cluster shapes. Such geometric validity functionals are:

• fuzzy partition density,

• fuzzy partition volume,

• class inertia,

• separation index.