Algebraic Models for Qualified Aggregation in General Rough Sets, and Reasoning Bias Discovery

TL;DR

This paper introduces algebraic models for combining elements in generalized rough sets over lattices, aiming to better understand reasoning biases and aggregation methods in uncertain and vague contexts.

Contribution

It develops novel algebraic models for acts of combination in rough sets over lattices, capturing skeptical, optimistic, and discriminatory reasoning behaviors.

Findings

Established fundamental results on weak negations and implications.

Model is suitable for studying toxic reasoning and machine learning biases.

Provides a framework for modeling diverse aggregation perspectives in rough set theory.

Abstract

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.