Rule-Induced Behavior of Fuzzy Scalar Objective Functions for Reliable Multi-Criteria Decision Making

What the math gives to ML

The paper identifies a concrete failure mode in rule-based scalarization: a model can appear to follow a reference merely because rule activations create broad flat plateaus, producing ambiguous selections rather than genuine preference minima. This is transferable to multi-objective neural training, where several normalized losses or constraint violations are often collapsed into one scalar objective and fixed weighted sums cannot express desirable, tolerable, and unacceptable regions. A practical adaptation is a differentiable three-class fuzzy loss aggregator with explicit output consequents, localized membership functions, and a diagnostic for plateau and tie ambiguity. The main test is whether it improves the intended task tradeoff and reference feasibility without merely changing the scale of the aggregate loss.