Aggregated Fuzzy Soft Rule Interaction and Root Mean Square (RMS) Based Acoustic Instability Modelling for Vocal Vulnerability Assessment

Abstract Vocal vulnerability assessment is challenging because acoustic deterioration often occurs gradually rather than through sharp diagnostic boundaries. Traditional threshold-based systems may therefore misrepresent transitional vocal states, while classical fuzzy inference models can lose clinically relevant information by suppressing weaker rule activations. This paper proposes an aggregated fuzzy soft rule interaction framework integrated with Root Mean Square (RMS)-based instability modelling for vocal vulnerability assessment. The aggregation operator incorporates all active fuzzy rule contributions, preserving subtle acoustic interactions, while the RMS instability measure quantifies oscillatory variability using dominant memberships derived from fundamental frequency and vocal perturbation index. Five theorems are rigorously established: boundedness of aggregation, monotonicity, boundedness of RMS instability, continuity, and perturbation stability. These results are proved for arbitrary dimensions involving p ≥ 1 acoustic parameters, qr ≥ 2 linguistic categories, and n ≥ 1 patients, showing that the framework is not restricted to the specific 3 × 3 = 9 rule structure used in the numerical study. Practical validity is illustrated through two numerical examples for each theorem. Statistical validation on 20 patient cases shows a strong positive correlation between aggregated rule interaction and RMS instability (r = 0.827, p < 0.001), while sensitivity analysis confirms the theoretical perturbation bound with Lipschitz constant L = 1. Diagnostic thresholds and algorithmic pseudocode are also provided to support reproducibility. The framework offers a mathematically rigorous and clinically interpretable approach to uncertainty-driven biomedical acoustic assessment. Keywords: Fuzzy-soft systems, Aggregated rule interaction, RMS instability modelling, Biomedical acoustics, Vocal vulnerability, Perturbation stability