Uncertainty of data, fuzzy membership functions, and multilayer perceptrons

摘要: Probability that a crisp logical rule applied to imprecise input data is true may be computed using fuzzy membership function (MF). All reasonable assumptions about uncertainty distributions lead MFs of sigmoidal shape. Convolution several inputs with uniform leads bell-shaped Gaussian-like functions. Relations between uncertainties and rules are systematically explored new types discovered. Multilayered perceptron (MLP) networks shown particular implementation hierarchical sets threshold logic based on MFs. They equivalent uncertainty. Leaving fuzziness the side makes or systems easier understand. Practical applications these ideas presented for analysis questionnaire gene expression data.