In this paper, we are mainly to solve the functional equations given by the modularity condition. Modularity condition between disjunctive (resp. conjunctive) uni-nullnorms and some most studied classes of binary aggregation operators (i.e., t-norms, t-conorms, uninorms and semi-t-operators) are discussed. Both positive and negative results of modularity condition for uni-nullnorms are obtained. Since uni-nullnorms are an extension of nullnorms and uninorms, previous results about modularity condition for nullnorms and uninorms in ${{𝒰}}_{max}$ and ${{𝒰}}_{min}$ can be obtained as simple corollaries.

中文翻译：

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Uni-Nullnorms 的模块化条件

本文主要是求解由模性条件给出的泛函方程。讨论了析取（resp. conjunctive）uni-nullnorms 和一些研究最多的二元聚合运算符类别（即 t-范数、t-conorms、uninorms 和 semi-t-运算符）之间的模块化条件。获得了 uni-nullnorms 的模块化条件的正面和负面结果。由于 uni-nullnorms 是 nullnorms 和 uninorms 的扩展，先前关于 nullnorms 和 uninorms 的模块化条件的结果${{𝒰}}_{最大限度}$和${{𝒰}}_{分钟}$可以作为简单的推论得到。