  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.
