Two roles of alpha-cut

John Yen (yen@cs.tamu.edu)
Sat, 30 Jan 1999 21:46:42 +0100 (MET)

This is regarding some of the discussions about alpha-cut.
There are at least two roles that alpha-cuts play in fuzzy logic.

1. Alpha cuts are used to decompose a fuzzy set into a weighted
combination of classical sets using the resolution identity
principle.

The principle is important in fuzzy set theory because it establishes
a bridge between fuzzy sets and crisp sets. Hence, it has been used
as the foundation for generalizing concepts and methods based on crisp
sets into those based on fuzzy sets.

2. Alpha cuts can be used to describe intermediate fuzzy conclusions
generated by fuzzy inference.

The first role, I think, is more important for understanding the
foundation of fuzzy logic.

Reference: J. Yen and R. Langari, ``Fuzzy Logic: Intelligence, Control,
and Information'', Prentice Hall, 1999.

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