Learning input-output fuzzy matrices from sensor data via Gaussian fuzzification

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.