What question did this study set out to answer?

This research aims to validate the Kerimov-Alekberli (KA) framework for modeling ethical stability in AI systems under uncertainty.

May 5, 2026Open Access

Ensuring Ethical Stability in Cyber-Physical Systems and Articial Intelligence Decisions: Simulation-Based Validation of the KerimovAlekberli (KA) Framework

Key Points

This research aims to validate the Kerimov-Alekberli (KA) framework for modeling ethical stability in AI systems under uncertainty.
Introduced a generalized ethical score incorporating bias and regulatory risk.
Validated the KA framework across five simulation environments.
Evaluated performance metrics like stability gain and reduced gender disparity scores.
Mean stability gain of ∆ = 0.040 across entropy regimes, increasing with entropy.
27.4% lower coefficient of variation and 55% faster entropy spike recovery than linear models.
Achieved a 28.8% reduction in gender disparity scores in fairness-sensitive classification.

Abstract

Articial intelligence systems deployed in high-stakes environments face a common structural challenge: decision quality degrades under uncertainty, and this degradation is rarely captured by aggregate accuracy metrics. The Kerimov-Alekberli (KA) framework addresses this challenge by modeling stability as an entropy-damped function of utility and internal structural properties. The generalized stability score E∗ = U − S/D, where D = 1 + γIint + λCa, moderates the destabilizing effect of entropy S through two internal structural proxies: internal integration Iint and aligned reective capacity Ca. This paper extends the KA framework in two directions. First, we introduce a generalized ethical score E = αU−βS−γB−δR, incorporating bias/fairness penalty B and regulatory risk R as additional ethical dimensions relevant to nancial, medical, and autonomous system deployment. Second, we validate both formulations across ve simulation environments: (1) a Markov chain stress test across three entropy regimes (n = 1000), (2) an adaptive threshold simulation with time-varying structural proxies (T = 200), (3) a competitor model comparison (n = 500), (4) a proxy interaction analysis across ve correlation levels, and (5) a credit/income classication fairness simulation (n = 5000, test n = 1500). Across all ve environments, the KA framework demonstrates consistent advantages: mean stability gain ∆ = 0 ̄ .040 across entropy regimes (monotonically increasing from 0.022 to 0.075 as entropy rises); 27.4% lower coecient of variation and 55% faster entropy spike recovery than the linear baseline; lowest coecient of variation among interpretable nonlinear models under high-entropy conditions; proxy independence maintained up to ρ(Iint, Ca) = 0.8; and a 28.8% reduction in gender disparity scores in fairness-sensitive classication. These results position the KA framework as a practically deployable, formally grounded stability metric for AI systems operating under uncertainty.

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