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Implications, coimplications and left semi-uninorms on a complete lattice | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 14، شماره 1، اردیبهشت 2017، صفحه 115-130 اصل مقاله (390.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3046 | ||
| نویسندگان | ||
| Yuan Wang1؛ Keming Tang1؛ Zhudeng Wang* 2 | ||
| 1College of Information Engineering, Yancheng Teachers University, Jiangsu 224002, People's Republic of China | ||
| 2School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, People's Republic of China | ||
| چکیده | ||
| In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $\vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $\wedge$-distributive left semi-uninorm, is the right residual implication induced by its $N$-dual operation. Then, we demonstrate that the $N$-dual operations of the left semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semi-uninorms. Finally, we reveal the relationships between conjunctive right arbitrary $\vee$-distributive left semi-uninorms induced by implications and disjunctive right arbitrary $\wedge$-distributive left semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle. | ||
| کلیدواژهها | ||
| Fuzzy connective؛ Implication؛ Coimplication؛ Left semi-uninorm؛ Neutrality principle | ||
| مراجع | ||
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