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

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance

A fuzzy dynamic model for total quality cost

This paper presents a dynamic Quality Cost Model capable of reconciling contributions of Juran’s traditional Model with those of the Zero Defects Model. Here, the cost functions depend on a company’s level of conformance in each period and at which stage of the Maturity Grid a company is positioned. To determine the stage at which the company is positioned on Crosby’s Maturity Grid, expert’s opinions will be considered using fuzzy logic to incorporate Hidden Quality Costs in the failure costs calculated by the company. The model will introduce exponential regression (ER) using Induced Ordered Weighted Average (IOWA). The results show that the learning process present in the proposed model leads it to evolve over time to positions that bring to mind the Zero Defects model. However, as appreciated in the case study, it can also regress and introduce the organisation into a level of saturation where the Cost of Quality is optimised before reaching perfection

Decision-making processes of non-life insurance pricing using fuzzy logic and OWA operators

Setting a commercial premium for an insurance policy is a complex process, even, though statistical tools provide fairly reliable information on the behavior of the frequency and cost of claims differentiated by risk profiles reflected in pure premium calculations. However lately setting the price the customer must pay has not been easy, because of the uncertainty of, having to use subjective criteria to analyze how demand may be affected by different price alternatives and economic situations. This article aims to develop this process in two stages. The first stage is carried out with the opinion of experts applied to uncertain numbers and Ordered Weighted Average (OWA) operators to assess the overall benefits of each profile to choose the best alternative. The second stage, which uses Heavy OWA (HOWA) operators, is based on the results obtained in the first stage and chooses a general price alternative for all profiles

Proposal for a Fuzzy Model to Assess Cost Overrun in Healthcare Due to Delays in Treatment

Apart from the effects of treating those infected with COVID‐19, the pandemic has also affected treatment for other diseases, which has been either interrupted or canceled. The aim of this paper is to provide a financial model for obtaining the cost overrun resulting from the worsening of illnesses and deaths for each of the causes considered. To achieve this, first deaths have been classified into causes of death and for each of these causes, an estimation has been made of the worsening condition of patients due to delay in treatment. Through these data, a fuzzy relation between deaths and the worsening condition of patients can be obtained. Next, the expertise process has been used to estimate cost overrun in relation to patients’ pathologies. The experts’ opinions have been aggregated using ordered weighted average (OWA). Lastly, using fuzzy logic again, a correction coefficient has been determined, which optimizes the future implementation of the proposed model without the need for a new estimation of inputs. The paper concludes with a numerical example for a better comprehension of the proposed theoretical model. Ultimately, it provides the scientific community in general and in particular managers of public administration entities with a novel tool for improving the efficiency of the healthcare system

Aggregation operators in group decision making: Identifying citation classics via H-classics

To analyze the past, present and future of a particular research field, classic papers are usually studied because they identify the highly cited papers being a relevant reference point in that specific research area. As a result of the possible mapping between high quality research and high citation counts, highly cited papers are very interesting. The objective of this study is to use the H-classics method, which is based on the popular h-index, to identify and analyze the highly cited documents published about aggregation operators in the research area of group decision making. According to the H-classics method, this research area is represented by 87 citation classics, which have been published from 1988 to 2014. Authors, affiliations (universities/institutions and countries), journals, books and conferences, and the topics covered by these 87 highly cited papers are studied.The authors would like to thank FEDER financial support from the Projects TIN2013-40658-P and TIN2016- 75850-P