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Construction of 2-uninorms on bounded lattices | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 15، دوره 19، شماره 1، فروردین و اردیبهشت 2022، صفحه 189-200 اصل مقاله (227.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6560 | ||
| نویسندگان | ||
| A. Xie* 1؛ Z. Yi2 | ||
| 1Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi, 330031, China | ||
| 2College of Mathematics and Information Science, Nanchang Normal University, Nanchang, Jiangxi, 330031, China | ||
| چکیده | ||
| Uninorms and nullnorms are special 2-uninorms. In this work, we construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U_1 and U_2, defined on sublattices [0,d] and [d,1], respectively, this paper presents two methods for constructing binary operators on L which extend both U_1 and U_2. We show that our first construction is a 2-uninorm on L if and only if U_2 is conjunctive and our second construction is a 2-uninorm on L if and only if U_1 is disjunctive. Moreover, we prove that the two 2-uninorms are, respectively, the weakest and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0,d]^2 and [d,1]^2 are respectively U_1 and U_2. | ||
| کلیدواژه‌ها | ||
| Bounded lattices؛ 2-uninorms؛ uninorms؛ nullnorms | ||
| مراجع | ||
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