The 2019 coronavirus disease outbreak, caused by the severe acute respiratory syndrome type-2 virus (SARS-CoV-2), was declared a pandemic in March 2020. Since its emergence to the present day, this disease has brought multiple countries to the brink of health care collapse during several waves of the disease. One of the most common tests performed on patients is chest x-ray imaging. These images show the severity of the patient’s illness and whether it is indeed covid or another type of pneumonia. Automated assessment of this type of imaging could alleviate the time required for physicians to treat and diagnose each patient. To this end, in this paper we propose the use of Convolutional Neural Networks (CNNs) to carry out this process. The aim of this paper is twofold. Firstly, we present a pipeline adapted to this problem, covering all steps from the preprocessing of the datasets to the generation of classification models based on CNNs. Secondly, we have focused our study on the modification of the information fusion processes of this type of architectures, in the pooling layers. We propose a number of aggregation theory functions that are suitable to replace classical processes and have shown their benefits in past applications, and study their performance in the context of the x-ray classification problem. We find that replacing the feature reduction processes of CNNs leads to drastically different behaviours of the final model, which can be benefitial when prioritizing certain metrics such as precision or recall.

Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this article, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from$L$to$L^{n}$and present a new similarity construction on$L^{n}$. proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.

Aggregation functions have been extensively studied and applied in several practical problems involving some sort of fuzzy modeling, by enacting the fusion process of data from the unit interval. T-norms and t-conorms, as well as overlap and grouping functions, are examples of pairs of aggregation functions that are related through the duality property, which is associated with some definition of fuzzy negation. By constructing pairs of dual aggregation functions and applying them in some practical problem, one can analyze which type of behaviour (conjunctive or disjunctive, for example) of the aggregation operator can benefit the whole system. However, when dealing with applications that do not involve fuzzy modeling, such as classification via convolutional neural networks, the data to be aggregated do not necessarily comes from the unit interval. Recently, a framework for defining classes aggregation functions on an arbitrary closed real interval (namely, (a, b)-aggregation functions) based on core known classes of aggregation functions have been introduced, but the study of negations and duality in this context is yet to be developed. Thus, in this paper we introduce and study the concept of negations defined on a arbitrary closed real intervals, called (a, b)-negations, presenting a construction method for them based core fuzzy negations. From that, we develop the concept of duality between (a, b)-aggregation functions, showing that the duality property is preserved when constructing (a, b)-aggregation functions from dual aggregation functions.

Traditionally, Convolutional Neural Networks make use of the maximum or arithmetic mean in order to reduce the features extracted by convolutional layers in a downsampling process known as pooling. However, there is no strong argument to settle upon one of the two functions and, in practice, this selection turns to be problem dependent. Further, both of these options ignore possible dependencies among the data. We believe that a combination of both of these functions, as well as of additional ones which may retain different information, can benefit the feature extraction process. In this work, we replace traditional pooling by several alternative functions. In particular, we consider linear combinations of order statistics and generalizations of the Sugeno integral, extending the latter's domain to the whole real line and setting the theoretical base for their application. We present an alternative pooling layer based on this strategy which we name "CombPool" layer. We replace the pooling layers of three different architectures of increasing complexity by CombPool layers, and empirically prove over multiple datasets that linear combinations outperform traditional pooling functions in most cases. Further, combinations with either the Sugeno integral or one of its generalizations usually yield the best results, proving a strong candidate to apply in most architectures.