一般粗糙集中限定聚合的代数模型及推理偏差发现
Algebraic Models for Qualified Aggregation in General Rough Sets, and Reasoning Bias Discovery
AI总结：
本文提出带近似算子格上的广义粗糙集代数聚合模型，以刻画悲观与乐观推理，并证明弱否定和蕴含结果，可用于发现推理偏差及学习歧视性行为的 ML 算法。
摘要：
在一般粗糙集的语境中，将两个事物结合以形成另一事物的行为并非直截了当。其他涉及不确定性与模糊性的理论也有类似情况。此类结合行为可被赋予额外含义，这些含义超越了结构性合取与析取，正如 $*$-范数理论及 $L$-模糊集上相关蕴含的情形。在本研究中，提出了在带近似算子的格（称为 rough convenience lattices，粗糙便利格）上的广义粗糙集中，事物结合行为的代数模型。该研究的强烈动机是希望对人类推理中的怀疑式或悲观式聚合，以及乐观式或可能性聚合进行建模，并且运算的选择受到该视角的约束。文中证明了最小模型所提供的弱否定与蕴含方面的基本结果。此外，该模型适合研究人类推理中的歧视性/有害行为，以及学习此类行为的 ML 算法。
英文摘要：
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.
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