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This paper shows fundamentals and applications of the parametric cerebellar model arithmetic computer (P-CMAC) network: a neural structure derived from the Albus CMAC algorithm and Takagi-Sugeno-Kang parametric fuzzy inference systems. It resembles the original CMAC proposed by Albus in the sense that it is a local network, (i.e., for a given input vector, only a few of the networks nodes-or neurons-will be active and will effectively contribute to the corresponding network output). The internal mapping structure is built in such a way that it implements, for each CMAC memory location, one linear parametric equation of the network input strengths. This mapping can be corresponded to a hidden layer in a multilayer perceptron (MLP) structure. The output of the active equations are then weighted and averaged to generate the actual outputs to the network. A practical comparison between the proposed network and other structures is, thus, accomplished. P-CMAC, MLP, and CMAC networks are applied to approximate a nonlinear function. Results show advantages of the proposed algorithm based on the computational efforts needed by each network to perform nonlinear function approximation. Also, P-CMAC is used to solve a practical problem at mobile telephony, approximating an RF mapping at a given region to help operational people while maintaining service quality.