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Representation of nullnorms on bounded lattices
Information Sciences ( IF 8.1 ) Pub Date : 2020-06-20 , DOI: 10.1016/j.ins.2020.06.013 Xiang-Rong Sun , Hua-Wen Liu
中文翻译:
有界格上零范数的表示
更新日期:2020-06-20
Information Sciences ( IF 8.1 ) Pub Date : 2020-06-20 , DOI: 10.1016/j.ins.2020.06.013 Xiang-Rong Sun , Hua-Wen Liu
Recently nullnorms on bounded lattices have been frequently investigated by many researchers. In this paper, we give the full characterization for quite a general class of nullnorms on bounded lattices and represent them by their underlying t-norms and t-conorms. An example is given to show the relationship between each block of the nullnorms. We also fully determine the values of arbitrary nullnorms when only one of the two variables is comparable with the absorbing elements. For the rest cases, we give some necessary conditions.
中文翻译:
有界格上零范数的表示
最近,许多研究人员经常研究有界晶格上的零范数。在本文中,我们对有界格子上的一类相当普遍的零范数进行全面描述,并用其下标的t范数和t-conorms表示它们。给出了一个示例以显示nullnorm的每个块之间的关系。当两个变量中只有一个与吸收元素相当时,我们也可以完全确定任意零范数的值。对于其余情况,我们给出一些必要条件。