On fuzzy clusterings with variable boundary conditions

Rok, strany: 2001, 31 - 50

Following Zadeh's approach, several authors restricted similarity relations to fuzzy equivalence relations where the transitivity is defined by using an arbitrary fixed t-norm. As we have shown, this approach leads to a very restricted concept of fuzzy partition (fuzzy clustering), which is too special for many applications. Taking into consideration these observations, we defined so-called $langle a,b,c angle$-clusterings, where $a$, $b$ and $c$ are fixed real numbers from the unit interval characterizing the disjointness, the normality, and the covering property of the given clustering, respectively. These clusterings are more general than partitions generated by fuzzy equivalence relations. But, again by applications, we have recognized that replacing the real numbers $a$, $b$ and $c$ by fuzzy sets $A$, $B$ and $C$ on the universe used (interpreted as “variable boundary conditions”) is very useful and enlarges the field of applicability of this clustering concept.

ISO 690:

Thiele, H. 2001. On fuzzy clusterings with variable boundary conditions. In Tatra Mountains Mathematical Publications, vol. 21, no.1, pp. 31-50. 1210-3195.

APA:

Thiele, H. (2001). On fuzzy clusterings with variable boundary conditions. Tatra Mountains Mathematical Publications, 21(1), 31-50. 1210-3195.