A Stochastic Model for Analyzing the Interpretability-Accuracy Trade-off in Interpretable Fuzzy Systems Using Nested Hyperball Structures

Our recent work proposed a new meaning preservation approach together with a parameterizable nested hyperball structured search space for interpretable fuzzy systems in order to solve a problem of inconsistency observed in conventional interpretable fuzzy knowledge bases and simultaneously to address the adjustment of the trade-off between interpretability and accuracy. Based on intuitive reasonings and simulation results a conjecture was formulated about favorable trade-off adjustment properties of the proposed method. The aim of the present paper is to construct a mathematical model, in which the conjectured properties can be analyzed and formally verified. Some computational considerations about the interpretation of the resulting knowledge bases are also made.