期刊
IEEE TRANSACTIONS ON FUZZY SYSTEMS
卷 26, 期 1, 页码 117-130出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2016.2639064
关键词
Crisp possibilistic mean value; fuzzy number; fuzzy restricted Boltzmann machine (FRBM); learning algorithm
资金
- National Natural Science Foundation of China [11401030, 61572540]
- Macau Science and Technology Development Fund [019/2015/A, 164/2014/SB/4052]
A fuzzy restricted Boltzmann machine (FRBM) is extended from a restricted Boltzmann machine (RBM) by replacing all the real-valued parameters with fuzzy numbers. A new FRBM that employs the crisp possibilistic mean value of a fuzzy number to defuzzify the fuzzy free energy function is presented. This approach is much clearer and easier to obtain the expression of the defuzzified free energy function and its approximation than the centroid method. Several theorems that discuss the error bounds of the approximation to ensure the rationality and validity are also investigated. Learning algorithms are given for the designed FRBM with symmetric triangular fuzzy numbers (STFNs), asymmetric triangular fuzzy numbers, and Gaussian fuzzy numbers. By appropriately choosing the parameters, a theorem is concluded that all FRBMs with symmetric fuzzy numbers will have identical learning algorithm to that of FRBMs with STFNs. This is illustrated by a case of FRBM with Gaussian fuzzy numbers. Two experiments including the MNIST handwriting recognition and the Bars-and-Stripes benchmark are carried out. The results show that the proposed FRBMs significantly outperform RBMs in learning accuracy and generalization ability, especially when encountering unlearned samples and recovering incomplete images.
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