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Self-dual pseudo-uninorms | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 23، شماره 2، خرداد و تیر 2026، صفحه 53-64 اصل مقاله (423.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.53842.9539 | ||
| نویسنده | ||
| Juraj Kalafut* | ||
| Dept. Mathematics, Slovak University of Technology, Radlisnkeho 11, 810 05 Bratislava, Slovakia | ||
| چکیده | ||
| Uninorms are a common generalization of t-norms and t-conorms, which are mutually dual aggregation functions. However, no uninorm is self-dual. In this paper, we show that dropping the axiom of commutativity allows a construction for self-dual pseudo-uninorms. We characterize three important classes of self-dual pseudo-uninorms, namely the representable pseudo-uninorms, pseudo-uninorms with all elements idempotent and those pseudo-uninorms that have both underlying functions continuous. Finally, it is proven that each self-dual pseudo-uninorm has continuous underlying functions. Note such a slight change has only a little effect on the continuity and commutativity of the pseudo-uninorm. | ||
| کلیدواژهها | ||
| Pseudo-uninorm؛ Uninorm؛ Self-duality؛ Semigroup؛ Strong negation | ||
| مراجع | ||
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