### Zusammenfassung

In this paper, the author introduces an a-cut based similarity condition (both in a weak and in a strong version) for fuzzy sets, originally presented by H. Frank. Based on this similarity condition, the author first shows that modeling with the standard trapezoid function is similar to modeling with the standard Pi-function. Then the author clarifies that modeling with general fuzzy sets (defined by a set of pairs) is similar to modeling with fuzzy sets using composed partitions of the standard quadratic membership functions (S-function, Z-function and Pi-function). Hence, there is more flexibility withchoosing between those membership functions. From a pratical point of view, it means that we can use linear membership functions instead of the standard quadratic membership functions if the concrete shape of the membership function is not determined exactly. In fuzzy systems, this flexibility has decisive advantages, especially if we have a high number of input dimensions.

### Referenz

MPS: Applied mathematics/0210004

Submitted: 02. October 2002

Classifications: Modelling and Simulation, Applied Mathematics, Control and Optimization

Comments: A4, 14 pages, english