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In this paper, we propose a novel state estimation plan using Adaptive Neuro-Fuzzy Inference System (ANFIS). To increase the speed and accuracy of estimation, an individual ANFIS is used for each bus. To improve the accuracy of training, the grasshopper optimization algorithm (GOA) is used for the training and optimization of ANFIS parameters. The main advantage of GOA training of ANFIS parameters is the increase in speed and accuracy in estimating power system state variables. One of the main features of the proposed design is its ability to provide an appropriate state estimation when incomplete data is sent to the control center due to the disconnection of communication or the failure of the measurement devices. The recovery of the missed data is implemented by the Group Method of Data Handling (GMDH) neural network. The GMDH neural network is widely used due to its proper speed for function estimation and approximation. Incomplete information obtained from measurements to estimate the state is processed by the GMDH neural network to recover lost information. The output of this neural network, which is the retrieval of complete measurement information, is given to ANFIS to estimate the state of the power system as input. [ABSTRACT FROM AUTHOR]