Fuzzy Euclidean Normed Spaces for Data Mining Applications

The aim of this paper is to introduce some special fuzzy norms on K n and to obtain, in this way, fuzzy Euclidean normed spaces. In order to introduce this concept we have proved that the cartesian product of a finite family of fuzzy normed linear spaces is a fuzzy normed linear space. Thus any fuzzy norm on K generates a fuzzy norm on K n . Finally, we prove that each fuzzy Euclidean normed space is complete. Fuzzy Euclidean normed spaces can be proven to be a suitable tool for data mining. The method is based on embedding the data in fuzzy Euclidean ( | | ) ∗ .