(2203-7279) A note on the ordinal sum of triangular norms on bounded lattices

	(2203-7279) A note on the ordinal sum of triangular norms on bounded lattices
Iranian Journal of Fuzzy Systems
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 اردیبهشت 1402 اصل مقاله (136.99 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7615
نویسندگان
T. Yan؛ Y. Ouyang^*
Faculty of Science, Huzhou University, Huzhou, Zhejiang 313000, China
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

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