Interpretable classifier design by axiomatic fuzzy sets theory and derivative-free optimization

Abstract

Axiomatic fuzzy sets (AFS) theory has seen extensive application in classification tasks in recent years. Yet, efficiently generating precise fuzzy descriptions for each target class from a multitude of complex concepts is challenging. This study aims to bridge this gap by transforming the challenge into a combinatorial optimization problem. We adopt an advanced model-based evolutionary optimization method, Randomized Coordinate Shrinking Classification (RACOS), to create an interpretable classifier within the AFS framework. By refining the definition of the complex concept set in AFS theory, we define a feasible search space for the optimization method. Innovative fitness functions have been developed focusing on semantic discrimination and prediction accuracy. Concurrently, we establish an encoding–decoding mechanism to link the solution vector with the complex concept for each fitness function. Ultimately, the complex concepts, guided by various fitness functions, are integrated into the class’s fuzzy description using AFS logical operations. Our method demonstrates competitive classification performance and superior interpretability compared to other evolutionary fuzzy rule-based classifiers.