A new type of generalized closed set via γ-open set in a fuzzy bitopological space

The aim of this paper is to study how distinct points and a point and a closed set not containing that points are separated by non overlapping open neighborhoods, in a bitopological space. The separation is studied with respect to a new type of $(1,2)\alpha$-open set together with a continuous function. We named the new axioms as star-ultra $T_{1}$, star-ultra $T_{2}$, star-ultra regular and normal. The star-ultra regular spaces is studied in two different ways and are called as A-star-ultra regular and B-star-ultra regular spaces.

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On Strongly b − θ -Continuous Mappings in Fuzzifying Topology

Mathematical Problems in Engineering ◽

10.1155/2021/3244618 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Ting Yang ◽

Ahmed Mostafa Khalil

Keyword(s):

Fuzzy Logic ◽

Continuous Mapping ◽

Topological Spaces ◽

Closed Set ◽

Open Set ◽

Neighborhood System ◽

Continuous Mappings ◽

Derived Set ◽

New Type

In this article, we will define the new notions (e.g., b − θ -neighborhood system of point, b − θ -closure (interior) of a set, and b − θ -closed (open) set) based on fuzzy logic (i.e., fuzzifying topology). Then, we will explain the interesting properties of the above five notions in detail. Several basic results (for instance, Definition 7, Theorem 3 (iii), (v), and (vi), Theorem 5, Theorem 9, and Theorem 4.6) in classical topology are generalized in fuzzy logic. In addition to, we will show that every fuzzifying b − θ -closed set is fuzzifying γ -closed set (by Theorem 3 (vi)). Further, we will study the notion of fuzzifying b − θ -derived set and fuzzifying b − θ -boundary set and discuss several of their fundamental basic relations and properties. Also, we will present a new type of fuzzifying strongly b − θ -continuous mapping between two fuzzifying topological spaces. Finally, several characterizations of fuzzifying strongly b − θ -continuous mapping, fuzzifying strongly b − θ -irresolute mapping, and fuzzifying weakly b − θ -irresolute mapping along with different conditions for their existence are obtained.

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Neutrosophic Soft Bitopological Spaces

International Journal of Neutrosophic Science ◽

10.54216/ijns.140104 ◽

2021 ◽

Author(s):

Ahmed B. AL-Nafee ◽

◽

Said Broumi ◽

Florentin Smarandache ◽

◽

...

Keyword(s):

Soft Set ◽

Topological Spaces ◽

Bitopological Space ◽

Closed Set ◽

Open Set ◽

Bitopological Spaces

In this paper, we built bitopological space on the concept of neutrosophic soft set, we defined the basic topological concepts of this spaces which are N3-(bi)*-open set, N3-(bi)*-closed set, (bi)*-neutrosophic soft interior, (bi)* neutrosophic soft closure, (bi)*-neutrosophic soft boundary, (bi)*-neutrosophic soft exterior and we introduced their properties. In addition, we investigated the relations of these basic topological concepts with their counterparts in neutrosophic soft topological spaces and we introduced many examples.

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DISCUSSION ON QUOTIENT BI-SPACE AND ON PAIRWISE REGULAR AND NORMAL SPACES IN BITOPOLOGICAL SPACES

Advances in Mathematical Sciences ◽

10.37516/adv.math.sci.2019.0051 ◽

2019 ◽

pp. 13-15

Author(s):

M. Arunmaran ◽

K. Kannan

Keyword(s):

Compact Subset ◽

Hausdorff Space ◽

Bitopological Space ◽

Closed Set ◽

Continuous Map ◽

Open Set ◽

Bitopological Spaces

In this paper, we introduce the concept “Quotient bi-space” in bitopological spaces. In addition, we investigate the results related with quotient bi-space. Moreover, we have discussed the results related with pairwise regular and normal spaces in bitopological space. For a non-empty set X, we can define two topologies (these may be same or distinct topologies) τ1 and τ2 on X. Then, the triple (X, τ1 , τ2 ) is known as bitopological space. Let (X, τ1 , τ2 ) be bitopological space, (Y, σ1 , σ2 ) be trivial bitopological space and f : (X, τ1 , τ2 ) → (Y, σ1 , σ2 ) be onto map. Then f is τ1 τ2 −continuous map. If η = {G (σ − open set in Y ) : f ^{−1} (G) is τ1 τ2 − open in X} then η is a topology on Y . Moreover, if (Y, σ, σ) be a quotient bi-space of (X, τ1 , τ2) under f : (X, τ1 , τ2 ) → (Y, σ, σ) and g : (Y, σ, σ) → (Z, η1 , η2 ) be a map, then, gis σ − continuous if and only if g ◦ f : (X, τ1 , τ2 ) → (Z, η1 , η2 ) is τ1 τ2 −continuous. Let (X, τ1 , τ2) be bitopological space and A be τ1 τ2 − compact subset of pairwise Hausdorff space X. Then, A is τ1 τ2 − closed set. Finally, we have discussed the following : Let (X, τ1 , τ2 ) be bitopological space and τ1 τ2 −compact pairwise Hausdorff space. Then, the space (X, τ1 , τ2 ) is pairwise normal.

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ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.41 ◽

2020 ◽

Vol 9 (11) ◽

pp. 9353-9360

Author(s):

G. Selvi ◽

I. Rajasekaran

Keyword(s):

Topological Spaces ◽

Closed Set ◽

Basic Properties ◽

Closed Sets ◽

New Class ◽

Open Set ◽

Continuous Maps

This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

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Synthetic speech detection through short-term and long-term prediction traces

EURASIP Journal on Information Security ◽

10.1186/s13635-021-00116-3 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Clara Borrelli ◽

Paolo Bestagini ◽

Fabio Antonacci ◽

Augusto Sarti ◽

Stefano Tubaro

Keyword(s):

Deep Learning ◽

Speech Processing ◽

Synthetic Speech ◽

Opinion Formation ◽

Closed Set ◽

Speech Detection ◽

Open Set ◽

Technological Advances ◽

Speech Generation ◽

Long Term Prediction

AbstractSeveral methods for synthetic audio speech generation have been developed in the literature through the years. With the great technological advances brought by deep learning, many novel synthetic speech techniques achieving incredible realistic results have been recently proposed. As these methods generate convincing fake human voices, they can be used in a malicious way to negatively impact on today’s society (e.g., people impersonation, fake news spreading, opinion formation). For this reason, the ability of detecting whether a speech recording is synthetic or pristine is becoming an urgent necessity. In this work, we develop a synthetic speech detector. This takes as input an audio recording, extracts a series of hand-crafted features motivated by the speech-processing literature, and classify them in either closed-set or open-set. The proposed detector is validated on a publicly available dataset consisting of 17 synthetic speech generation algorithms ranging from old fashioned vocoders to modern deep learning solutions. Results show that the proposed method outperforms recently proposed detectors in the forensics literature.

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Mosquito species identification using convolutional neural networks with a multitiered ensemble model for novel species detection

Scientific Reports ◽

10.1038/s41598-021-92891-9 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Adam Goodwin ◽

Sanket Padmanabhan ◽

Sanchit Hira ◽

Margaret Glancey ◽

Monet Slinowsky ◽

...

Keyword(s):

Neural Networks ◽

Species Identification ◽

Convolutional Neural Networks ◽

Novel Species ◽

Novelty Detection ◽

Mosquito Species ◽

Image Database ◽

Closed Set ◽

Open Set

AbstractWith over 3500 mosquito species described, accurate species identification of the few implicated in disease transmission is critical to mosquito borne disease mitigation. Yet this task is hindered by limited global taxonomic expertise and specimen damage consistent across common capture methods. Convolutional neural networks (CNNs) are promising with limited sets of species, but image database requirements restrict practical implementation. Using an image database of 2696 specimens from 67 mosquito species, we address the practical open-set problem with a detection algorithm for novel species. Closed-set classification of 16 known species achieved 97.04 ± 0.87% accuracy independently, and 89.07 ± 5.58% when cascaded with novelty detection. Closed-set classification of 39 species produces a macro F1-score of 86.07 ± 1.81%. This demonstrates an accurate, scalable, and practical computer vision solution to identify wild-caught mosquitoes for implementation in biosurveillance and targeted vector control programs, without the need for extensive image database development for each new target region.

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EvidentialMix: Learning with Combined Open-set and Closed-set Noisy Labels

2021 IEEE Winter Conference on Applications of Computer Vision (WACV) ◽

10.1109/wacv48630.2021.00365 ◽

2021 ◽

Author(s):

Ragav Sachdeva ◽

Filipe R. Cordeiro ◽

Vasileios Belagiannis ◽

Ian Reid ◽

Gustavo Carneiro

Keyword(s):

Closed Set ◽

Open Set ◽

Noisy Labels

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On topological properties of weakly m-convex sets

Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine ◽

10.37069/1683-4720-2020-34-8 ◽

2021 ◽

Vol 34 ◽

pp. 75-84

Author(s):

Tetiana Osipchuk

Keyword(s):

Convex Sets ◽

Convex Set ◽

Topological Classification ◽

Connected Components ◽

Topological Properties ◽

Convex Domains ◽

Closed Set ◽

Dimensional Plane ◽

Open Set ◽

Plane Passing

The topological properties of classes of generally convex sets in multidimensional real Euclidean space $\mathbb{R}^n$, $n\ge 2$, known as $m$-convex and weakly $m$-convex, $1\le m<n$, are studied in the present work. A set of the space $\mathbb{R}^n$ is called \textbf{\emph{$m$-convex}} if for any point of the complement of the set to the whole space there is an $m$-dimensional plane passing through this point and not intersecting the set. An open set of the space is called \textbf{\emph{weakly $m$-convex}}, if for any point of the boundary of the set there exists an $m$-dimensional plane passing through this point and not intersecting the given set. A closed set of the space is called \textbf{\emph{weakly $m$-convex}} if it is approximated from the outside by a family of open weakly $m$-convex sets. These notions were proposed by Professor Yuri Zelinskii. It is known the topological classification of (weakly) $(n-1)$-convex sets in the space $\mathbb{R}^n$ with smooth boundary. Each such a set is convex, or consists of no more than two unbounded connected components, or is given by the Cartesian product $E^1\times \mathbb{R}^{n-1}$, where $E^1$ is a subset of $\mathbb{R}$. Any open $m$-convex set is obviously weakly $m$-convex. The opposite statement is wrong in general. It is established that there exist open sets in $\mathbb{R}^n$ that are weakly $(n-1)$-convex but not $(n-1)$-convex, and that such sets consist of not less than three connected components. The main results of the work are two theorems. The first of them establishes the fact that for compact weakly $(n-1)$-convex and not $(n-1)$-convex sets in the space $\mathbb{R}^n$, the same lower bound for the number of their connected components is true as in the case of open sets. In particular, the examples of open and closed weakly $(n-1)$-convex and not $(n-1)$-convex sets with three and more connected components are constructed for this purpose. And it is also proved that any compact weakly $m$-convex and not $m$-convex set of the space $\mathbb{R}^n$, $n\ge 2$, $1\le m<n$, can be approximated from the outside by a family of open weakly $m$-convex and not $m$-convex sets with the same number of connected components as the closed set has. The second theorem establishes the existence of weakly $m$-convex and not $m$-convex domains, $1\le m<n-1$, $n\ge 3$, in the spaces $\mathbb{R}^n$. First, examples of weakly $1$-convex and not $1$-convex domains $E^p\subset\mathbb{R}^p$ for any $p\ge3$, are constructed. Then, it is proved that the domain $E^p\times\mathbb{R}^{m-1}\subset\mathbb{R}^n$, $n\ge 3$, $1\le m<n-1$, is weakly $m$-convex and not $m$-convex.

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Auditory Training and Speech Discrimination

Journal of Speech and Hearing Research ◽

10.1044/jshr.1304.839 ◽

1970 ◽

Vol 13 (4) ◽

pp. 839-855 ◽

Cited By ~ 18

Author(s):

Daniel L. Bode ◽

Herbert J. Oyer

Keyword(s):

Auditory Discrimination ◽

Auditory Training ◽

Speech Discrimination ◽

Training Material ◽

Closed Set ◽

Open Set ◽

Speech Reception ◽

Hearing Aid Use ◽

Response Formats ◽

Respective Type

Thirty-two adults with sensorineural hearing loss participated in a short-term auditory training program. The listeners were assigned to one of four matched groups which were equivalent in pure-tone sensitivity, speech-reception threshold, PB discrimination in quiet and in noise, intelligence, age, education, duration of loss, sex, and hearing-aid use. Each group responded during training to a different combination of listening condition (S/N varied or S/N-constant) and speech material (closed-set or open-set response formats). Statistically significant increase in auditory discrimination was shown on the W-22 and Rhyme tests, while the increase revealed by the Semi-Diagnostic test was not significant. Results indicated that the two listening conditions were equally effective. Similarly, the two types of training material brought about equivalent increases in overall speech discrimination. Trends suggested that open-set and closed-set training each had most effect on the respective type of speech discrimination. In addition, improvement in auditory discrimination was associated with those individuals who were oldest, with those who had highest intelligence, and with those who responded to training material at the most intense presentation level. Finally, listeners who reported the most hearing handicap also tended to show the greatest loss in speech reception and in speech discrimination in noise.

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