A fuzzy and neuro-fuzzy approach to modelling cattle grazing on pastures with low stocking rates in Central Europe

This paper describes a fuzzy and neuro-fuzzy approach to spatial explicit modelling of cattle grazing intensity in temperate zones in Central Europe on pastures with low stocking rates. The aim was to create a simple model based on datasets that could be collected as easily as possible in order to predict the grazing intensity. Large-scale moderate cattle grazing has been introduced in many areas across Europe as a low cost management initiative for the restoration or conservation of open landscapes. As a consequence of the heterogeneity and large size of the pastures under investigation, the relationships between the various investigated factors are often poorly understood and the data collected have a high degree of uncertainty. A fuzzy approach was selected which allowed for operation with vague knowledge and data of high uncertainty. Two fuzzy rule-based models of extensive grazing are presented in this paper. The first is a model based on the Mamdani-type of inference. The linguistic rules of this model were formulated by a domain expert. The second is a model based on the Sugeno-type rules and on a given input-output dataset. The number of rules and the initial membership function parameters were established by a simple and effective clustering algorithm (subtractive clustering). Using the neuronal network technique (ANFIS), optimal model parameters were identified. These parameters minimize the root mean squared error of the model. A dataset of a pasture in North Germany was used as training data for an ANFIS learning procedure. In order to check the generalization capability of the two models, the grazing intensity predicted by both models was compared with grazing intensity data gathered on three pastures over two years. The Mamdani- and Sugeno-type models were implemented using the Fuzzy Logic Toolbox of MATLAB©. The results of both models confirm a suitability of these models for the modelling of cattle grazing.