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Commutative, associative and non-decreasing functions continuous around diagonal | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 4، دوره 19، شماره 2، خرداد و تیر 2022، صفحه 31-48 اصل مقاله (249.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6786 | ||
| نویسنده | ||
| A. Mesiarová-Zemánková* | ||
| Mathematical Institute, Slovak Academy of Sciences, 81473 Bratislava, Slovakia | ||
| چکیده | ||
| We characterize all functions that can be obtained as a $z$-ordinal sum of semigroups related to continuous t-norms, t-conorms, representable uninorms and idempotent semigroups. We show that this class of functions is bigger than the class of $n$-uninorms with continuous underlying functions. Vice versa, we show that the characterization of $n$-uninorms with continuous underlying functions via $z$-ordinal sum can be extended to any commutative, associative and non-decreasing binary function on the unit interval, which has continuous Archimedean components and is continuous on the diagonal. | ||
| کلیدواژه‌ها | ||
| n-uninorm؛ ordinal sum؛ z-ordinal sum؛ representable uninorm؛ t-norm؛ t-conorm؛ nullnorm | ||
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آمار تعداد مشاهده مقاله: 262 تعداد دریافت فایل اصل مقاله: 303 |
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