Predicting crop yields using a new robust Bayesian averaging model based on multiple hybrid ANFIS and MLP models

Predicting crop yield is an important issue for farmers. Food security is important for decision-makers. The agriculture industry can more accurately supply human demand for food if the crop yield is predicted accurately. Tomato is one of the most important crops so that 160 million tonnes of tomatoes are produced annually around the world. In this study, tomato yield based on data of 40 cities of Iran country including annual average temperature (T), relative humidity (RH), effective rainfall (R), wind speed (WS), and Evapotranspiration (EV) for the period of 1968–2018 was predicted using a new Bayesian model averaging (BMA). The paper's main innovation is the use of the new BMA so that it allows the modellers to quantify the uncertainty of model parameters and inputs simultaneously. For this aim, first, the multiple Adaptive neuro-fuzzy interface system (ANFIS) and multi-layer perceptron (MLP) were used for predicting crop yield. To train the ANFIS and MLP model, a new algorithm, namely, multi verse optimization algorithm (MOA) was used. Also, the ability of MOA was benchmarked against the particle swarm optimization (PSO), and firefly algorithm (FFA). In the next level, the new BMA used the outputs of the ANFIS-MOA, MLP-MOA, ANFIS, FFA, MLP-FFA, ANFIS-PSO, MLP-PSO, ANFIS, and MLP for predicting tomato yield in an ensemble framework. The five- input combination of RH, T, and R, WS, and EV gave the best result. The mean absolute error (MAE) of the BMA in the testing level was 20.12 (Ton/ha) while it was 24.12, 24.45, 24.67, 25.12, 29.12, 30.12, 31.12, and 33.45 for the ANFIS-MOA, MLP-MOA, ANFIS-FFA, MLP-FFA, ANFIS-PSO, MLP-PSO, ANFIS, and MLP models. Regarding the results of uncertainty analysis, the uncertainty of BMA was lower than those of the ANFIS-MOA, MLP-MOA, ANFIS-FFA, MLP-FFA, ANFIS-PSO, MLP-PSO, ANFIS, and MLP models while the MLP model provided the highest uncertainty. The results of this study indicated that BMA using multiple MLP and ANFIS model was useful for predicting tomato yield.