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Our aim is to obtain a suitable characterization of certain topological properties of a random closed set through its capacity functional. The main technique mixes two different fields: on the one hand, the abstract simplicial complex associated to a covering, whose topology coincides with the topology of the original set thanks to the nerve theorem. On the other hand, the celebrated Choquet-Kendall-Matheron theorem, which states that a random closed set is characterized by its capacity functional.

Let $\kappa$ be an uncountable cardinal with $\kappa=\kappa^{{\kappa^+$'' implies the statement "every closed subset of ${}^\kappa\kappa$ is a continuous image of ${}^\kappa(\kappa^+)$'' or its negation., Comment: 30 pages

Most of the existing synthetic aperture radar (SAR) automatic target recognition (ATR) methods aim at the closed set situation, in which the classes of targets in the test set have appeared in the training set. However, in practice, the classifier is likely to encounter the targets from unseen categories and classify them incorrectly, which brings a huge challenge to current SAR ATR techniques. To overcome this problem, this letter proposes an open set recognition (OSR) method based on multitask learning, and the method is developed from generative adversarial network (GAN). Essentially, this method decomposes OSR into two tasks: classification and abnormal detection. The classification task is the same as that in the closed set situation, while the abnormal detection task is used to determine whether the targets belongs to the unseen categories. Correspondingly, the network structure of GAN is modified and the other full-connection network branch is added to the end of the discriminator, so it has the ability to accomplish the above two tasks. Finally, according to the results of two tasks, the OSR for SAR targets can be realized. The experimental results on moving and stationary target acquisition (MSTAR) dataset demonstrate that the proposed method has the better recall, precision, F1, and accuracy than other OSR methods.

Real-world applications now deal with a massive amount of data, and information about the world is inaccurate, incomplete, or uncertain. Therefore, we present in our paper a proposed model for solving problems. This model is based on the class of locally generalized closed sets, namely, locally simply* alpha generalized closed* sets and locally simply* alpha generalized closed** sets (briefly, L S-M*alpha GC*-sets and L S-M*alpha GC**-sets), based on simply* alpha open set. We also introduce various concepts of their properties and their relationship with other types, and we are studying several of their properties. Finally, we apply the concept of the simply* alpha open set to illustrate the importance of our method in decision-making for information systems about the infections of Coronavirus in humans. In fact, we were able to decide the impact factors of Coronavirus infection. The results were also programmed using the MATLAB program. Therefore, it is recommended that our proposed concept be used in future decision-making.

The purpose of this paper is to define and study a new class of sets called micro generalized closed sets and define micro generalized continuous function and irresolute micro generalized continuous function in micro topological spaces. Basic properties of micro generalized closed sets and its characterizations are analyzed.

In this paper, the properties of ψgs-closed sets in bitopological spaces are investigated. The relationships between ψgs-closed set and other closed sets in bitopological spaces are established and some properties of ψgs-closure and ψgs-interior are provided.

Rough set theory is a granular computing tool used to deal with ambiguity and uncertainty in information systems. However, many optimization problems in rough sets, such as attribute reduction, are NP-hard problems, and most of the algorithms for these problems are greedy. As a complex mathematical structure, matroids provide a powerful tool for solving combinatorial optimization problems related to attribute reduction. Therefore, it is necessary to study the combination of matroids and rough sets. This paper uses rough sets and matrix approaches to spanning matroids. Moreover, the features of spanning matroids are applied to attribute reduction in decision information systems. Firstly, we construct spanning sets based on equivalence relations which can induce matroids called spanning matroids. Secondly, some features of spanning matroids, such as closed sets, bases, are studied by matrix method. Finally, the judgment theorems with the features of spanning matroids are proposed for addressing the problems about attribute reduction in decision information systems. Simultaneously, the sufficient and necessary conditions for distinguishing upper approximation reduction in inconsistent decision information systems are obtained from the viewpoint of spanning matroids.

In this paper, we generalize the concept of a monotone convergence space (also called a d-space) to the setting of a Q -cotopological space, where Q is a commutative and integral quantale. We establish a D-completion for every stratified Q -cotopological space, which is a category reflection of the category S Q -CTop of stratified Q -cotopological spaces onto the full subcategory S Q -DCTop of monotone convergence Q -cotopological spaces. By introducing the notion of a tapered set, a direct characterization of the completion is obtained: the D-completion of each stratified Q -cotopological space X consists exactly of those tapered closed sets in X. We show that the D-completion can be applied to obtain a universal fuzzy directed completion of a Q -ordered set by endowing it with the Scott cotopology, taking the D-completion, and then passing to the specialization Q -order. Consequently, the category Q -DOrd of fuzzy directed complete Q -ordered sets and Scott continuous functions is reflective in the category Q -Ordσ of Q -ordered sets and Scott continuous functions.

In this paper, the concept of soft closed groups is presented using the soft ideal pre-generalized open and soft pre-open, which are -ᶅ- - -closed sets " -closed", Which illustrating several characteristics of these groups. We also use some games and - Separation Axiom, such as (Ʈ0, Ӽ, ᶅ) that use many tables and charts to illustrate this. Also, we put some proposals to study the relationship between these games and give some examples.

Except a closed set $${\mathfrak {S}}^c$$ with zero parabolic Hausdorff measure, the weak limit $$(\rho ,\mathbf{u})$$ of approximate solutions is a renormalized weak solution with finite energy of three dimensional compressible Navier–Stokes equations for $$\gamma \in (6/5, 3/2]$$ as constructed by Lions and Feireisl et al. in the Leray sense. The key novelty of the paper is the improved integrability of pressure by localization, which is based on the faster decay of the gradient of velocity and the higher integrability of the Riesz potentials of both density and momentum.

Algorithms based on Close-by-One (CbO) are polynomial delay algorithms used for the enumeration of closed sets, particularly formal concepts in Formal Concept Analysis. We describe and categorize their distinctive features. We experimentally evaluate the influence of the features on the computation time. We show that via the study of individual features, we can design new and more efficient algorithms.

Nano JD closed sets, a new class of Nano generalized closed sets in Nano topological spaces, relies on the g-interior and g closure operators. This paper aims to interpret and investigate its extension and connection with other existing concepts.

We extend, to the framework of topological vector spaces, two results by Horvath and Kuratowski related to conditions for a family of closed sets to have compact and nonempty intersection. This extension enables us to introduce a number of applications such as the existence of maximal elements in preordered spaces, issues related to KKM functions, fixed point theorems, a variant of a matching theorem by Fan, and mainly the improvement of some minimax and variational inequalities.

The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively closed subsets of a ring with the help of graph theory. A particular attention is paid to constructions of subsets of a given diameter. In particular, we compute the diameter of artinian semisimple algebras.

The aim of the present article is to introduce the concepts of $$s_{p}-$$ convergent sequence in generalized intuitionistic fuzzy metric spaces, i.e., $${\mathscr {L}}$$ -fuzzy metric spaces and analyze relations of convergence, $$s_{p}-$$ convergence, $$s_{\infty }-$$ convergence and $$st-$$ convergence in $${\mathscr {L}}$$ -fuzzy metric spaces. Further, we examine $$s_{p}-$$ convergence, $$s_{\infty }-$$ convergence and $$st-$$ convergence using the subsequence of convergent sequence for above-stated spaces. We finally define $$s_{p}-$$ closed sets, $$s_{\infty }-$$ closed sets and $$st-$$ closed sets in intuitionistic fuzzy metric spaces and investigate relations of them.

It is known that the Hurwitz zeta-function $$\zeta(s,\alpha)$$ with transcendental or rational parameter $$\alpha$$ has a discrete universality property; i.e., the shifts $$\zeta(s+ikh,\alpha)$$ , $$k\in\mathbb N_0$$ , $$h> 0$$ , approximate a wide class of analytic functions. The case of algebraic irrational $$\alpha$$ is a complicated open problem. In the paper, some progress in this problem is achieved. It is proved that there exists a nonempty closed set $$F_{\alpha,h}$$ of analytic functions such that the functions in $$F_{\alpha,h}$$ are approximated by the above shifts. Also, the case of certain compositions $$\Phi(\zeta(s,\alpha))$$ is discussed.

The concept of neutrosophic continuous function was very first introduced by A.A. Salama et al. The main aim of this paper is to introduce a new concept of Neutrosophic continuous function namely Strongly Neutrosophic gsα* - continuous functions, Perfectly Neutrosophic gsα* - continuous functions and Totally Neutrosophic gsα* - continuous functions in Neutrosophic topological spaces. These concepts are derived from strongly generalized neutrosophic continuous function and perfectly generalized neutrosophic continuous function. Several interesting properties and characterizations are derived and compared with already existing neutrosophic functions.

[ES] Se presenta un conjunto cerámico excepcional localizado en el yacimiento hispanorromano de Contributa Iulia Ugultunia (Medina de las Torres, Badajoz). Además de un análisis en clave tipocronológica de las piezas, se estudia el contexto espacial en el que se localizó, donde se destaca la presencia de un edificio singular. Este estudio nos ha permitido, por un lado, aportar nuevas precisiones cronotipológicas de la vajilla y otros enseres localizados, gracias a la naturaleza unifásica del vertido. Por otro, se presenta una hipótesis de trabajo relativa al acto convivial que generó la deposición y su relación con las prácticas religiosas de este enclave. Para finalizar, este singular hallazgo se pone en relación con otros conjuntos excepcionales hallados en la misma región geográfica, la Baeturia céltica, lo que nos permite trazar algunos patrones de comportamiento común en este espacio del suroroeste peninsular., [EN] An exceptional ceramic ensemble located in the Hispano-Roman site of Contributa Iulia Ugultunia (Medina de las Torres, Badajoz) is presented. In addition to a typochronological analysis of the pieces, the spatial context in which it was lo-cated is studied, where the presence of a unique building stands out. This study has allowed us, on the one hand, to provide new chronotypological details of the crockery and other localized items, thanks to the one-phase nature of the spill. On the other, a working hypothesis is presented regarding the convivial act that generated the deposition and its relationship with the religious practices of this settlement. Finally, this singular finding is studied in relation with other exceptional assemblages found in the same geographical region, the Celtic Baeturia, which allows us to trace some common behavior patterns in this area of the south-west of the Iberian peninsula., Este trabajo es el resultado del proyecto Corpus Vasorum Hispanorum. Analisis tipológi-co, cronológico y prosopográfico de los sigilla en terra sigillata hispánica a partir de los centros consumidores. Parte I: Lusitania (PGC2018-093478-A-I00 – Convocatoria Proyectos de Excelencia – Plan Estatal de Generación de Conocimiento – Ministerio de Ciencia, Innovación y Universidades – España.

Anomaly classification can provide a discrimination of the type of anomaly at hand, that can help the user to narrow down the search space during troubleshooting. A limitation of most machine learning (ML) classification models is being under the closed set assumption and thereby failing to recognize unknown data. Literature refers to this issue as the Opens Set Recognition (OSR) problem. In this paper, the given use case is the detection of technical faults in HVAC systems in commercial buildings. Here, the OSR problem is of high relevance, because it is very unrealistic that all possible faults are already known beforehand. This paper proposes an ML pipeline for open set anomaly classification. To address the OSR problem, the pipeline makes use of three common neural network architecture models that successively build on each other, namely two autoencoders and one ANN classifier. The advantage of using common well-known models is the ease of implementation for solution developers. The validation is made against an HVAC dataset published by LBNL that contains 7 fault cases, where we assume 3 of them as unknown. Our validation results show that the proposed pipeline can significantly reduce the risk of false class predictions in the presence of unknown data.

We introduce the concept of d*g?-closed sets in a topological space and investigate their properties. Moreover, we investigate new separation axioms and new functions in topological spaces.

In this paper, we have proposed a robust Printed Circuit Board (PCB) classification system based on computer vision and deep learning to assist sorting e-waste for recycling. We have used a public PCB dataset acquired using a conveyor belt, as well as a locally developed PCB dataset that represents challenging practical conditions such as varying lighting, orientation, distance from camera, cast shadows, view-points and different cameras/resolutions. A pre-trained EfficientNet-B3 deep learning model is utilized and retrained for use with our data in PCB classification context. Deep nets are designed for closed set recognition tasks capable of classifying only the images they have been trained for. We have extended the closed set nature of deep nets for use in our open set classification tasks which require identifying unknown PCBs apart from classifying known PCBs. We have achieved an open set average accuracy of 92.4% which is state of the art given the complexities in the datasets we worked with.

For the existing Closed Set Recognition (CSR) methods mistakenly identify unknown jamming signals as a known class, a Conditional Gaussian Encoder (CG-Encoder) for 1-dimensional signal Open Set Recognition (OSR) is designed. The network retains the original form of the signal as much as possible and deep neural network is used to extract useful information. CG-Encoder adopts residual network structure and a new Kullback-Leibler (KL) divergence is defined. In the training phase, the known classes are approximated to different Gaussian distributions in the latent space and the discrimination between classes is increased to improve the recognition performance of the known classes. In the testing phase, a specific and effective OSR algorithm flow is designed. Simulation experiments are carried out on 9 jamming types. The results show that the CSR and OSR performance of CG-Encoder is better than that of the other three kinds of network structures. When the openness is the maximum, the open set average accuracy of CG-Encoder is more than 70%, which is about 30% higher than the worst algorithm, and about 20% higher than the better one. When the openness is the minimum, the average accuracy of OSR is more than 95%.

Thermal face recognition has various applications in security, video-surveillance, military and government industries, etc. In contrast to the visible-light domain case, there is a lack of sufficiently large databases of thermal-face images. Therefore, it is difficult to construct a good face recognition system directly through learning procedures. We address this problem by using the synthesis approach, in which artificial visible-domain images of faces are generated from thermal face images and then identified in the visible-light domain. The generation of the artificial face images is done using a conditional Generative Adversarial Network, and the face identification is done by another, separate, deep neural network. Generating visible face images from thermal ones using DNNs requires large datasets of pairs of thermal and visible face images of the same persons, taken from the same position, time and imaging conditions, with two different cameras. The available datasets of such pairs are of relatively very low amount of subjects. Therefore, as in other similar studies, we approach this problem as a closed-set face recognition task, in which all testing identities are predefined in the training set. We train the face identification network itself using the synthesized images together with the original ground-truth visible-domain images to create a recognition system that is suitable to the characteristics of the artificially generated images. Thus, the recognition network will be optimized specifically for the thermal face recognition.

The aim of this paper is to introduce the concepts of IFS \(_{\alpha}\) -open sets. Also we discussed the relationship between this type of Open set and other existing Open sets in Intuitionistic fuzzy topological spaces. Also we introduce new class of closed sets namely IFS \(_{\alpha}\) -closed sets and its properties are studied.