The law of importation is an important property of fuzzy implication functions because of its interesting applications in approximate reasoning and image processing. In this paper, as a continuation of the paper [S. Massanet, D. Ruiz-Aguilera, and J. Torrens, “Characterization of a class of fuzzy implication functions satisfying the law of importation with respect to a fixed uninorm—Part I,” IEEE Trans. Fuzz Syst. , to be published.], the characterization of all fuzzy implication functions that satisfy the law of importation with respect to a given uninorm $U$ , and having an $\alpha$-section that is a continuous fuzzy negation is given for the cases when the uninorm $U$ lies in one of the most used classes of uninorms. As the case when the uninorm $U$ is in ${\mathcal U}_{\min }$ was already solved in [S. Massanet, D. Ruiz-Aguilera, and J. Torrens, “Characterization of a class of fuzzy implication functions satisfying the law of importation with respect to a fixed uninorm—Part I,” IEEE Trans. Fuzz Syst., to be published.], this paper focuses in the cases when $U$ is an idempotent uninorm, a representable uninorm, or a uninorm continuous in the open unit square.

中文翻译：

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一类满足输入律的模糊蕴涵函数的刻画（第二部分）

输入定律是模糊蕴涵函数的一个重要性质，因为它在近似推理和图像处理中的应用很有趣。在本文中，作为论文 [S. Massanet、D. Ruiz-Aguilera 和 J. Torrens，“一类模糊蕴涵函数的特征满足关于固定单范式的输入定律——第一部分，”IEEE 翻译 模糊系统。, 待发表。], 满足关于给定单范式的输入定律的所有模糊蕴涵函数的表征 $U$ ，并且有一个 $\alpha$- 部分是一个连续的模糊否定给出的情况下 $U$ 属于最常用的单范式之一。当不规则时的情况$U$ 在 ${\mathcal U}_{\min }$已经在 [S. Massanet、D. Ruiz-Aguilera 和 J. Torrens，“一类模糊蕴涵函数的特征满足关于固定单范式的输入定律——第一部分，”IEEE 翻译 模糊系统。，待发表。]，本文重点讨论以下情况 $U$ 是幂等单项、可表示单项或在开单位方格中连续的单项。