A fuzzy backpropagation algorithm

This paper presents an extension of the standard backpropagation algorithm (SBP). The proposed learning algorithm is based on the fuzzy integral of Sugeno and thus called fuzzy backpropagation (FBP) algorithm. Necessary and sufficient conditions for convergence of FBP algorithm for single-output networks in case of single- and multiple-training patterns are proved. A computer simulation illustrates and confirms the theoretical results. FBP algorithm shows considerably greater convergence rate compared to SBP algorithm. Other advantages of FBP algorithm are that it reaches forward to the target value without oscillations, requires no assumptions about probability distribution and independence of input data. The convergence conditions enable training by automation of weights tuning process (quasi-unsupervised learning) pointing out the interval where the target value belongs to. This supports acquisition of implicit knowledge and ensures wide application, e.g. for creation of adaptable user interfaces, assessment of products, intelligent data analysis, etc.

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