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A note on the ordinal sum of triangular norms on bounded lattices | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 20، شماره 4، مهر و آبان 2023، صفحه 75-80 اصل مقاله (137.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.41885.7279 | ||
| نویسندگان | ||
| Tingsu Y Yan؛ Yao Y Ouyang* | ||
| Faculty of Science, Huzhou University | ||
| چکیده | ||
| The ordinal sum construction is an important way to generate new triangular norms (t-norms for short) on real unit interval from existing ones. Saminger extended the ordinal sum construction of t-norms to bounded lattices in a direct way and proved that, except for very special cases the ordinal sum of t-norms on bounded lattices may be not a t-norm. To ensure the ordinal sum of t-norms is always a t-norm, several modified ordinal sum of t-norms have been developed. This note reviews several such constructions. As a byproduct, we point out that some recent results concerning ordinal sum of t-norms by A\c{s}ici can be seen as corollaries of these construction. | ||
| کلیدواژه‌ها | ||
| Bounded lattices؛ Triangular norms؛ Ordinal sum | ||
| مراجع | ||
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