Flexible Neuro Fuzzy Systems英文电子书.pdf

554 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 14, NO. 3, MAY 2003 Flexible Neuro-Fuzzy Systems Leszek Rutkowski, Senior Member, IEEE, and Krzysztof Cpalka Abstract—In this paper, we derive new neuro-fuzzy structures It should be emphasized that formulas (1) and (2) do called flexible neuro-fuzzy inference systems or FLEXNFIS. not satisfy the conditions of fuzzy implication formu- Based on the input–output data, we learn not only the parameters lated by Fodor [11]. We refer to (1) and (2) as to “engi- of the membership functions but also the type of the systems (Mamdani or logical). Moreover, we introduce: 1) softness to neering implications” (see Mendel [34], [35]) contrary to fuzzy implication operators, to aggregation of rules and to the fuzzy implications satisfying the axiomatic definition connectives of antecedents; 2) certainty weights to aggregation (see Definition 1). of rules and to connectives of antecedents; and 3) parameterized The aggregation is performed by an application of families of T-norms and S-norms to fuzzy implication operators, S-norm to aggregation of rules and to connectives of antecedents. Our approach introduces more flexibility to the structure and design of neuro-fuzzy systems. Through computer simulations, we show (4) that Mamdani-type systems are more suitable to approximation e.g., problems, whereas logical-type systems may be preferred for classification problems.