Abstract
An adaptive fuzzy system with sinusoidal membership functions is introduced in this chapter. Functional equivalence between multilayered neural networks and a fuzzy system with a singleton fuzzifier, a product inference, a centroid defuzzifter, and a sinusoidal membership function is discussed in this paper. Fuzzy basis function expansions of a multi-input and singal output (MISO) fuzzy systems are given in order to describe the input-output relationships of fuzzy systems. Then, sinusoidal membership functions are introduced for fuzzy systems with a graded value over [0, 1]. Learning algorithms for tuning both network weights and parameters of sinusoidal membership functions are discussed. Finally, a simulation example of nonlinear system identification is provided to demonstrate the effectiveness of such an adaptive fuzzy system
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Jin, L., Gupta, M.M. (1998). Adaptive Fuzzy Systems With Sinusoidal Membership Functions. In: Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach . International Series in Intelligent Technologies, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5473-8_18
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DOI: https://doi.org/10.1007/978-1-4615-5473-8_18
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