Algebraic Models for Qualified Aggregation in General Rough Sets, and Reasoning Bias Discovery
This work addresses the challenge of modeling skeptical and optimistic aggregation in reasoning, with applications to bias discovery in AI, but it appears incremental as it builds on existing rough set and lattice theories.
The research tackled the problem of modeling qualified aggregation in general rough sets by inventing algebraic models for acts of combining things in rough convenience lattices, proving fundamental results on weak negations and implications. The result includes a model suitable for studying discriminatory behavior in human reasoning and ML algorithms.
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.