Value-transformation for monotone prediction by approximating fuzzy membership functions

Monotone prediction problems, in which the target variable is non-decreasing given an increase of the explanatory variables, have became more popular nowadays in many problem settings which fulfill the so-called monotonicity constraint, namely, if an object is better in all attributes as another one then it should not be classified lower. Recent approaches to monotone prediction consider linear ordering on attribute domains, thus the meaning of being better in an attribute is limited to having a larger or a lower value in that attribute. However, this limitation restricts the use of recent approaches in cases where middle or marginal values of an attribute are better, what is natural in many real-world scenarios. We present a simple attribute value-transformation approach in this paper. The idea is to map attribute domains to real values where the mapped values express how the given value of an attribute contributes to higher classification of objects. Thus, we are searching for an data-specific approximation of a fuzzy membership function on the domain of each (numerical) attribute. Then, instead of the original attribute values we use their mapped values to mitigate the violation of monotonicity constraints in the data. Our approach is quite simple and is not limited to numerical attributes only. The described approach was tested and evaluated on benchmark datasets from the UCI machine learning repository.