Possibilistic Clustering Enabled Neuro Fuzzy Logic

Artificial neural networks are a dominant force in our modern era of data-driven artificial intelligence. The adaptive neuro fuzzy inference system (ANFIS) is a neural network based on fuzzy logic versus a more traditional premise like convolution. Advantages of ANFIS include the ability to encode and potentially understand machine learned neural information in the pursuit of explainable, interpretable, and ultimately trustworthy artificial intelligence. However, real-world data is almost always imperfect, e.g., incomplete or noisy, and ANFIS is not naturally robust. Specifically, ANFIS is susceptible to over inflated uncertainty, poor antecedent (fuzzy set) data alignment, degenerate optimization conditions, and hard to interpret logic, to name a few factors. Herein, we explore the use of possibilistic clustering to identify outliers, specifically typicality degrees, to increase the robustness of ANFIS; or any fuzzy logic neuron/network. Experiments are presented that demonstrate the need and quality of the proposed solutions in the pursuit of robust interpretable machine learned neuro fuzzy logic solutions.

I. Introduction

The world is once again fixated on neural nets, due in large part to their recent performance leaps across numerous application domains; computer vision, natural language processing, etc. On the other hand, modern deep learning has a list of equally deep concerns, e.g., are we really just engineering machines that discover desirable correlations versus underlying causations [1]. Regardless, in all this excitement the field has more-or-less converged into a single mathematical foundation, convolution; which powers more complicated constructs like residual and recurrent networks. Furthermore, the vast majority of these deep nets have given rise to black box solutions– that have little emphasis on explainability or interpretability. Herein, we focus on a non-convolutional contribution from the field of fuzzy set theory, the adaptive neuro-fuzzy inference system (ANFIS) [2]. Specifically, we focus on a first order (linear) Takagi-Sugeno-Kang (TSK) type ANFIS.