3,462 research outputs found

    Aggregation functions: Means

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    The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).

    Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks

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    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

    Fuzzy Techniques for Decision Making 2018

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    Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

    Blind restoration of images with penalty-based decision making : a consensus approach

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    In this thesis we show a relationship between fuzzy decision making and image processing . Various applications for image noise reduction with consensus methodology are introduced. A new approach is introduced to deal with non-stationary Gaussian noise and spatial non-stationary noise in MRI

    EXPLAINABLE FEATURE- AND DECISION-LEVEL FUSION

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    Information fusion is the process of aggregating knowledge from multiple data sources to produce more consistent, accurate, and useful information than any one individual source can provide. In general, there are three primary sources of data/information: humans, algorithms, and sensors. Typically, objective data---e.g., measurements---arise from sensors. Using these data sources, applications such as computer vision and remote sensing have long been applying fusion at different levels (signal, feature, decision, etc.). Furthermore, the daily advancement in engineering technologies like smart cars, which operate in complex and dynamic environments using multiple sensors, are raising both the demand for and complexity of fusion. There is a great need to discover new theories to combine and analyze heterogeneous data arising from one or more sources. The work collected in this dissertation addresses the problem of feature- and decision-level fusion. Specifically, this work focuses on fuzzy choquet integral (ChI)-based data fusion methods. Most mathematical approaches for data fusion have focused on combining inputs relative to the assumption of independence between them. However, often there are rich interactions (e.g., correlations) between inputs that should be exploited. The ChI is a powerful aggregation tool that is capable modeling these interactions. Consider the fusion of m sources, where there are 2m unique subsets (interactions); the ChI is capable of learning the worth of each of these possible source subsets. However, the complexity of fuzzy integral-based methods grows quickly, as the number of trainable parameters for the fusion of m sources scales as 2m. Hence, we require a large amount of training data to avoid the problem of over-fitting. This work addresses the over-fitting problem of ChI-based data fusion with novel regularization strategies. These regularization strategies alleviate the issue of over-fitting while training with limited data and also enable the user to consciously push the learned methods to take a predefined, or perhaps known, structure. Also, the existing methods for training the ChI for decision- and feature-level data fusion involve quadratic programming (QP). The QP-based learning approach for learning ChI-based data fusion solutions has a high space complexity. This has limited the practical application of ChI-based data fusion methods to six or fewer input sources. To address the space complexity issue, this work introduces an online training algorithm for learning ChI. The online method is an iterative gradient descent approach that processes one observation at a time, enabling the applicability of ChI-based data fusion on higher dimensional data sets. In many real-world data fusion applications, it is imperative to have an explanation or interpretation. This may include providing information on what was learned, what is the worth of individual sources, why a decision was reached, what evidence process(es) were used, and what confidence does the system have on its decision. However, most existing machine learning solutions for data fusion are black boxes, e.g., deep learning. In this work, we designed methods and metrics that help with answering these questions of interpretation, and we also developed visualization methods that help users better understand the machine learning solution and its behavior for different instances of data
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