Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multi-layer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy and our previously established XAI indices shed light on the quality of our data, model, and its decisions.Comment: IEEE Transactions on Fuzzy System

Operational Risk Management using a Fuzzy Logic Inference System

Operational Risk (OR) results from endogenous and exogenous risk factors, as diverse and complex to assess as human resources and technology, which may not be properly measured using traditional quantitative approaches. Engineering has faced the same challenges when designing practical solutions to complex multifactor and non-linear systems where human reasoning, expert knowledge or imprecise information are valuable inputs. One of the solutions provided by engineering is a Fuzzy Logic Inference System (FLIS). Despite the goal of the FLIS model for OR is its assessment, it is not an end in itself. The choice of a FLIS results in a convenient and sound use of qualitative and quantitative inputs, capable of effectively articulating risk management's identification, assessment, monitoring and mitigation stages. Different from traditional approaches, the proposed model allows evaluating mitigation efforts ex-ante, thus avoiding concealed OR sources from system complexity build-up and optimizing risk management resources. Furthermore, because the model contrasts effective with expected OR data, it is able to constantly validate its outcome, recognize environment shifts and issue warning signals.Operational Risk, Fuzzy Logic, Risk Management Classification JEL:G32, C63, D80

Determine OWA operator weights using kernel density estimation

Some subjective methods should divide input values into local clusters before determining the ordered weighted averaging (OWA) operator weights based on the data distribution characteristics of input values. However, the process of clustering input values is complex. In this paper, a novel probability density based OWA (PDOWA) operator is put forward based on the data distribution characteristics of input values. To capture the local cluster structures of input values, the kernel density estimation (KDE) is used to estimate the probability density function (PDF), which fits to the input values. The derived PDF contains the density information of input values, which reflects the importance of input values. Therefore, the input values with high probability densities (PDs) should be assigned with large weights, while the ones with low PDs should be assigned with small weights. Afterwards, the desirable properties of the proposed PDOWA operator are investigated. Finally, the proposed PDOWA operator is applied to handle the multicriteria decision making problem concerning the evaluation of smart phones and it is compared with some existing OWA operators. The comparative analysis shows that the proposed PDOWA operator is simpler and more efficient than the existing OWA operator