Spline Optimization of Soft Connectives in Machine Learning Models

Abstract

In this study, the problem of limited accuracy of machine learning models using soft logical connectives is investigated. Such connectives have shown their effectiveness in models with fuzzy initial data. On the one hand, the fundamental disadvantage of soft connectives is their non-associativity. On the other hand, the disadvantages of the currently used soft connectives include the loss of monotonicity and the inability to control several factors simultaneously. All these problems have been solved by the authors. We have proposed an approximation of the signum function by a ?1-smooth spline. The first part of the spline is responsible for the curvature of the connective at the diagonal and is adjustable. The second part of the spline is the solution to the optimization problem. We minimized the difference between the connective and the associative connective, the latter in our study was the minimum function. In the resulting solution, the rate of deviation reduction is the highest among known connectives. We have achieved not only a small deviation from associativity, but also the presence of a large domain of exact associativity. This area is up to a third of the volume of all triples of arguments. A comparative analysis of the currently used soft connectives with the constructed model was carried out. It was shown that the spline approximation is able to reduce the influence of all negative factors and is more flexible in setting. Moreover, the constructed spline model allows numerous modifications depending on the factor that requires the most attention for different tasks.