arXiv cs.AI· P. A. Golovinski, A. A. Drobyshev, A. O. Shatalova·· 1 天前AI 评分18
用模糊选择性状态模型预测消费者偏好动态
Fuzzy selective state model for forecasting the dynamics of consumer preferences
AI 导读
研究者提出一种 Mamba 型选择性状态空间模型，其隐藏状态为三角模糊数，在 Matveev 双分量模糊数代数中运算，递推参数由清晰特征计算、模糊部分保持非负系数线性，从而保证状态始终是合规三角模糊数且为历史观测的凸组合，模糊度不随时间累积。
正文 · 原文
Abstract:We consider forecasting the dynamics of consumer preferences of retail chain customers. A customer's preference is described by a triangular fuzzy number. The evolution of the preference over time is governed by a Mamba-type selective state space model whose hidden state is a triangular number, with computations carried out in M.G.~Matveev's two-component algebra of fuzzy numbers. The recurrence parameters are computed from crisp features, while the fuzzy part of the model remains linear with non-negative coefficients. We show that the state then always remains a proper triangular number and is a convex combination of past observations, so that the fuzziness of the forecast does not accumulate over time and the algebraic computations coincide with Zadeh's extension principle. On a synthetic example with competitor promotions and customer switching, a lightweight 107-parameter model reaches a mean absolute error of the forecast centre of 0.154 versus 0.163 for the constant-inertia evolution operator and 0.179 for the naive forecast, matches a crisp model of the same architecture and additionally provides a linguistically interpretable estimate of forecast vagueness. We also show how the linguistic readout of the forecast can be used to detect a permanent switch of a customer to a competitor.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.41879 [cs.AI] |
| (or arXiv:2610.41879v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.41879 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Pavel Golovinski [view email]
[v1]
Fri, 30 Oct 2026 15:27:14 UTC (733 KB)
来源：arXiv cs.AI · arxiv.org