Sustainable Rangeland Management Using a Multi-Fuzzy Model : How to Deal with Heterogeneous Experts' Knowledge

While fuzzy specialists usually use homogeneous experts' knowledge to construct fuzzy models, it is much more difficult to deal with knowledge elicited from a heterogeneous group of experts. This issue especially holds in the area of the sustainable rangeland management. One way to deal with the diversity of opinions is to develop a fuzzy system for all experts and to combine all these so-called primary systems into one multi-fuzzy model. To derive each of the primary fuzzy systems using the knowledge of a group of administrative experts, several semi-structured interviews were held in three different areas of the Fars province in Southwest Iran. In order to find the final output of the multi-fuzzy model, we applied different voting' methods. The first method simply uses the arithmetic average of the primary outputs as the final output of the multifuzzy model. This final output represents an estimation of the Right Rate of Stocking. We also propose other (un)supervised voting methods. Most importantly, by harmonizing the primary outputs such that outliers get less emphasis, we introduce an unsupervised voting method calculating a weighted estimate of the Right Rate of Stocking. This harmonizing method is expected to provide a new useful tool for policymakers in order to deal with heterogenity in experts' opinions: it is especially useful in cases where little field data is available and one is forced to rely on experts' knowledge only. By constructing the three fuzzy models based on the elicitation of heterogeneous experts' knowledge, our study shows the multidimensional vaguenesses that exist in sustainable rangeland management. Finally, by comparing the final Right Rate of Stocking with its medium range, this study proves the existence of overgrazing in pastures of the three regions of the Fars province in Southwest Iran. Keywords: sustainable rangeland management, carrying capacity, multi-fuzzy model, heterogeneous