# mk:fic04

### Summary

*Soft Data Fusion by N-th Degree T-Norms*. Mario Köppen. In Proceedings of the Intl. Workshop on Fuzzy Systems and Innovational Computing (CD-ROM), pages 290-295, Kitakyushu, Japan, 2004.

### Abstract

The extension of the set operation mink (maxk) of selection of the $k$-th smallest (largest) element to fuzzy sets is considered. The extension is based on the provision of set operators purely based on subset selection, and maximum and minimum operators. Then, all or part of all maximum and minimum operators can be replaced by corresponding pairs of T- and S-norms. There are only a few cases where such an approach is still preserving sufficient mathematical properties, including recursiveness of the mink operation. The approach based on $min2=max(min(a_{j}|j \ne i)|1 \le i \le n)$ for a set $(a_{i})$ of $n$ real values from 0,1$ is considered in more detail, and applied in an example manner to the definition of an image operator. The fact that Tk-norms provide larger values than the (often very small values of) T-norms, from which they are derived, offers a lot of practical applications for Tk-norms, e.g. in fuzzy control, neuro-fuzzy systems, and computing-with-words.

### Bibtex entry

`@INPROCEEDINGS { mk:fic04,`

ABSTRACT = { The extension of the set operation mink (maxk) of selection of the $k$-th smallest (largest) element to fuzzy sets is considered. The extension is based on the provision of set operators purely based on subset selection, and maximum and minimum operators. Then, all or part of all maximum and minimum operators can be replaced by corresponding pairs of T- and S-norms. There are only a few cases where such an approach is still preserving sufficient mathematical properties, including recursiveness of the mink operation. The approach based on $min2=max(min(a_{j}|j \ne i)|1 \le i \le n)$ for a set $(a_{i})$ of $n$ real values from 0,1$ is considered in more detail, and applied in an example manner to the definition of an image operator. The fact that Tk-norms provide larger values than the (often very small values of) T-norms, from which they are derived, offers a lot of practical applications for Tk-norms, e.g. in fuzzy control, neuro-fuzzy systems, and computing-with-words. },

ADDRESS = { Kitakyushu, Japan },

AUTHOR = { Mario Köppen },

BOOKTITLE = { Proceedings of the Intl. Workshop on Fuzzy Systems and Innovational Computing (CD-ROM) },

MODIFIED = { 2008-02-28 14:21:31 +0900 },

EDITOR = { SOFT, Japan },

HASABSTRACT = { Yes },

PAGES = { 290--295 },

PDF = { fic04.pdf },

TITLE = { Soft Data Fusion by N-th Degree T-Norms },

YEAR = { 2004 },

}