Application of fuzzy logic to Boolean models for digital soil assessment

Boolean models based on expert knowledge are often used to classify soils into a limited number of classes of a difficult-to-measure soil attribute. Although the primary data used for these classifications contain information on whether the soil is a typical class member or a boundary case between two classes, this is not retained in the final result. Such information is relevant in land use planning and soil management as it enables more flexible decision taking, but in the pre-digital era it was unfeasible to prevent the loss of it. We can now retain this information by fuzzifying the Boolean model using fuzzy logic. Choices must then be made on the type of membership function, logical operators, and formulation of the assessment rules. From a review of the main types of membership functions we conclude that piecewise linear functions are most appropriate in practical applications. Combinations of different fuzzy union (or) and intersection (and) connectives were tested on a 2-dimensional example. Nearly all combinations gave results that partly contradict the associated a priori knowledge, the exception being the Bounded sum connective for or, and the Product connective for and. We also found that in formulating the rules, overlap of predictor classes and negation should be avoided. Unrestricted choice of fuzzy connectives and rule formulation will generally lead to inconsistencies. The selected methods were tested in two case studies: one on suitability for seed-potatoes in an Italian region and one on suitability for grass farming in a Dutch region. The maps produced with the fuzzy and Boolean models are broadly similar. However, maps from the fuzzy models indicate that some areas represent a transition between two original Boolean classes, thereby providing relevant additional information. In the case study on seed-potatoes the quantitative prediction errors of the original Boolean suitability map were greatly reduced by the fuzzification.

► We investigated how soil assessment tables can best be fuzzified.
► Max and min functions in fuzzy rules showed adverse effects, not sum and product.
► Fuzzified suitability tables for grass and seed-potato gave better suitability maps.