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

Xiefei He; Tao Yu; Zicong He; Shi'an Wang; Xiefei He; Tao Yu; Zicong He; Shi'an Wang

doi:10.3934/era.2026140

Electronic Research Archive

2026, Volume 34, Issue 5: 3093-3111. doi: 10.3934/era.2026140

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Theory article

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

1.
College of Information Engineering, Guangzhou Institute of Technology, Guangzhou 510075, China
2.
School of Manufacturing, Guangdong Polytechnic of Science and Trade, Guangzhou 511500, China
3.
Guangdong Industry Polytechnic University, Guangzhou 510300, China

Received: 13 January 2026 Revised: 24 February 2026 Accepted: 16 March 2026 Published: 09 April 2026

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.
- fuzzy matrix,
- max-min composition,
- Gaussian membership functions,
- differentiable smoothing,
- stochastic gradient descent,
- sensor-driven fuzzy modelling
Citation: Xiefei He, Tao Yu, Zicong He, Shi'an Wang. Learning input-output fuzzy matrices from sensor data via Gaussian fuzzification[J]. Electronic Research Archive, 2026, 34(5): 3093-3111. doi: 10.3934/era.2026140

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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.

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