@article{He2026, 
author = {Xiefei He and Tao Yu and Zicong He and Shi'an Wang},
title = {Learning input-output fuzzy matrices from sensor data via Gaussian fuzzification},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {5},
pages = {3093-3111},
keywords = {fuzzy matrix, max-min composition, Gaussian membership functions, differentiable smoothing, stochastic gradient descent, sensor-driven fuzzy modelling},
url = {https://www.sciopen.com/article/10.3934/era.2026140},
doi = {10.3934/era.2026140},
abstract = {Fuzzy relation matrices are a core representation mechanism in fuzzy inference and fuzzy system modeling, yet practical data are often raw multichannel sensor readings rather than pre-defined input/output fuzzy vectors. We develop an end-to-end supervised learning framework that (i) maps sensor readings to fuzzy vectors via per-channel Gaussian fuzzification and (ii) learns a max-min fuzzy relation matrix from adjacent-time sensor pairs. To overcome the nonsmooth max-min composition, we introduce a differentiable softmax/softmin surrogate with temperature annealing and derive a stochastic-gradient training procedure that jointly optimizes the relation matrix and fuzzifier parameters. Experiments on structured synthetic sensor streams show stable convergence and improved structure recovery over a fixed (data-driven) fuzzifier baseline while approaching an oracle fuzzifier.}
}