In the context of general rough sets, the act of combining two things to form another is not straightforward. The situation is similar for other theories that concern uncertainty and vagueness. Such acts can be endowed with additional meaning that go beyond structural conjunction and disjunction as in the theory of $*$-norms and associated implications over $L$-fuzzy sets. In the present research, algebraic models of acts of combining things in generalized rough sets over lattices with approximation operators (called rough convenience lattices) is invented. The investigation is strongly motivated by the desire to model skeptical or pessimistic, and optimistic or possibilistic aggregation in human reasoning, and the choice of operations is constrained by the perspective. Fundamental results on the weak negations and implications afforded by the minimal models are proved. In addition, the model is suitable for the study of discriminatory/toxic behavior in human reasoning, and of ML algorithms learning such behavior.

翻译：在一般粗糙集的背景下，将两个事物组合以形成另一事物的操作并非显而易见。对于其他涉及不确定性和模糊性的理论，情况类似。此类操作可被赋予超越结构合取与析取的额外意义，如$L$-模糊集上$*$-范数理论及其相关蕴含算子所体现的那样。本研究在带有近似算子的格（称为粗糙便利格）上，发明了广义粗糙集中事物组合操作的代数模型。该研究强烈受限于建模人类推理中怀疑或悲观、乐观或可能聚合的动机，操作的选择受该视角约束。本文证明了最小模型所支持的弱否定与蕴含算子的基本结果。此外，该模型适用于研究人类推理中的歧视/毒性行为，以及学习此类行为的机器学习算法。