Adaptive fuzzy cognitive maps with hybrid optimization for predicting sales in conditions of market volatility

Purpose. Development and validation of the adaptive NCC methodology with hybrid weight optimization and dynamic correction of membership functions for unstable markets.

Methods. The methodology includes a proposal for a three-level NCC architecture (5 inputs, 4 hidden nodes, 3 outputs) initialized by the Saaty method with a consistency ratio of CR=0.038; hybrid weight optimization combining the particle swarm algorithm (PSO) and adaptive regularization; and quarterly adaptation of trapezoidal membership functions based on streaming clustering using Streaming C-means and exponential smoothing (EMA).

Results. The results of testing on data from the retail chain N (time span of 62 weeks, 345 observations) showed: high prediction accuracy with MAPE 7.2% (95% confidence interval [6.8;7.6]), which is statistically significantly lower (p<0.01) than the errors of the LSTM (9.8%) and static NCC (15.8%) models, and is comparable to the accuracy of XGBoost (7.8%, p=0.12), while adaptive NCC provides superiority in the interpretability of causal relationships (for example, the weight of the marketing budget's impact on sales w₁₁=0.78±0.05); increased robustness, resulting in a smaller increase in forecast error during the March shock period (+49.2% for adaptive NCC versus +86.9% for LSTM); and significant economic efficiency, confirmed by the results of implementation in the ERP system: reduction of logistics costs by 15.2% (absolute savings of 5.1 million rubles), reduction of inventory turnover from 18.3 to 15.1 days, quarterly ROI of 287.5% and estimated net present value (NPV) of the project 9.2 million rubles (95% CI [8.1;10.3].

Conclusion. The developed methodology provides highly accurate, interpretable, and robust sales forecasting in unstable market conditions, proving its practical effectiveness and economic feasibility. Promising areas of development include the automation of map construction using GANs, the acceleration of calculations through CUDA implementation, and the integration with graph neural networks (GNN).

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