Soft Intersection Research Articles

Soft-int Almost Interior Ideals for Semigroups

Just as the concept of interior ideal of semigroups is a generalization of ideal in semigroups, the notion of soft intersection (soft-int) interior ideal is a generalization of soft-int ideal. In this paper, we propose the concepts of soft-int (weakly) almost interior ideal of a semigroup as a generalization of the nonnull soft-int interior ideals. We explore their algebraic properties in detail. We also show that an idempotent soft-int almost interior ideal is a soft-int almost subsemigroup. We additionally derive several intriguing relations related to semiprimeness, minimality, and (strongly) primeness between almost interior ideals and soft-int almost interior ideals.

SOFT INTERSECTION ALMOST QUASI-INTERIOR IDEALS OF SEMIGROUPS

Similar to how the quasi-interior ideal generalizes the ideal and interior ideal of a semigroup, the concept of soft intersection quasi-interior ideal generalizes the idea of soft intersection ideal and soft intersection interior ideal of a semigroup. In this study, we provide the notion of soft intersection almost quasi-interior ideal as well as the soft intersection weakly almost quasi-interior ideal in a semigroup. We show that any nonnull soft intersection quasi-interior ideal is a soft intersection almost quasi-interior ideal; and soft intersection almost quasi-interior ideal is a soft intersection weakly almost quasi-interior ideal, but the converses are not true. We further demonstrate that any idempotent soft intersection almost quasi-interior ideal is a soft intersection almost subsemigroup. With the established theorem that states that if a nonempty set A is almost quasi-interior ideal, then its soft characteristic function is a soft intersection almost quasi-interior ideal, and vice versa, we are also able to derive several intriguing relationships concerning minimality, primeness, semiprimeness, and strongly primeness between almost quasi-interior ideals, and soft intersection almost quasi-interior ideals.

Soft intersection almost ideals of semigroups

The aim of this study is to present the notion of soft intersection almost left (respectively, right) ideal of a semigroup which is a generalization of nonnull soft intersection left (respectively, right) ideal of a semigroup and investigate the related properties in detail. We show that every idempotent soft intersection almost (left/right) ideal is a soft intersection almost subsemigroup. Besides, we acquire remarkable relationships between almost left (respectively, right) ideals and soft intersection almost left (respectively, right) ideals of a semigroup as regards minimality, primeness, semiprimeness and strongly primeness.

Soft intersection almost subsemigroups of semigroups

Semigroups are the building blocks of algebra as they have application in automata, coding the-ory, formal languages, and theoretical computer science. They are also used in the solutions of graph theory and optimization theory. For the advanced study of algebraic structures and their applications, ideals are essential. The generalization of ideals in algebraic structures is necessary for further research on algebraic structures. The main purpose of this paper is to present the notion of soft intersection almost subsemigroup of a semigroup, which is a generalization of soft intersection subsemigroup and investigate its basic pro-perties in detail. In this context, we also obtain many striking relationships between almost subsemigroups and soft intersection almost subsemigroups concerning minimality, primeness, semiprimeness and strongly primeness.

ATS-YOLOv7: A Real-Time Multi-Scale Object Detection Method for UAV Aerial Images Based on Improved YOLOv7

The objects in UAV aerial images have multiple scales, dense distribution, and occlusion, posing considerable challenges for object detection. In order to address this problem, this paper proposes a real-time multi-scale object detection method based on an improved YOLOv7 model (ATS-YOLOv7) for UAV aerial images. First, this paper introduces a feature pyramid network, AF-FPN, which is composed of an adaptive attention module (AAM) and a feature enhancement module (FEM). AF-FPN reduces the loss of deep feature information due to the reduction of feature channels in the convolution process through the AAM and FEM, strengthens the feature perception ability, and improves the detection speed and accuracy for multi-scale objects. Second, we add a prediction head based on a transformer encoder block on the basis of the three-head structure of YOLOv7, improving the ability of the model to capture global information and feature expression, thus achieving efficient detection of objects with tiny scales and dense occlusion. Moreover, as the location loss function of YOLOv7, CIoU (complete intersection over union), cannot facilitate the regression of the prediction box angle to the ground truth box—resulting in a slow convergence rate during model training—this paper proposes a loss function with angle regression, SIoU (soft intersection over union), in order to accelerate the convergence rate during model training. Finally, a series of comparative experiments are carried out on the DIOR dataset. The results indicate that ATS-YOLOv7 has the best detection accuracy (mAP of 87%) and meets the real-time requirements of image processing (detection speed of 94.2 FPS).

Substation Personnel Fall Detection Based on Improved YOLOX

With the continuous promotion of smart substations, staff fall detection has become a key issue in automatic detection of substations. The injuries and safety hazards caused by falls among substation personnel are numerous. If a timely response can be made in the event of a fall, the injuries caused by falls can be reduced. In order to address the issues of low accuracy and poor real-time performance in detecting human falls in complex substation scenarios, this paper proposes an improved algorithm based on YOLOX. A customized feature extraction module is introduced to the YOLOX feature fusion network to extract diverse multiscale features. A recursive gated convolutional module is added to the head to enhance the expressive power of the features. Meanwhile, the SIoU(Soft Intersection over Union) loss function is utilized to provide more accurate position information for bounding boxes, thereby improving the model accuracy. Experimental results show that the improved algorithm achieves an mAP value of 78.45%, which is a 1.31% improvement over the original YOLOX. Compared to other similar algorithms, the proposed algorithm achieves high accuracy prediction of human falls with fewer parameters, demonstrating its effectiveness.

A study of soft hyperideals in right regular LA-semihypergroups

Although a lot of work has been done by algebraist on soft set theory and hyperstructure theory, several fundamental results of soft intersection hyperideals in LA-semihypergroups remained untouched. This paper aims at studying some structural properties of LA-semihypergroups by applying soft set theory. In this paper, we define right regular LA-semihypergroups and introduce the concept of soft generalized bi-hyperideals in LA-semihypergroups. Further, we characterize right regular LA-semihypergroups in terms of different kinds of soft right hyperideals, soft left hyperideals and soft generalized bi-hyperideals. Idempotent soft hyperideals in LA-semihypergroups are introduced and some related results on them are obtained. It is proved that in an LA-semihypergroup with left identity, the collection of all soft left hyperideals, which are idempotent forms a commutative monoid. Examples are provided to illustrate the results.

A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals

In recent years, soft sets have become popular in various fields. For this reason, many studies have been carried out in the field of algebra. In this study, soft intersection k-ideals are defined with the help of a semiring, and some algebraic structures are examined. Moreover, the quotient rings are defined by k-semiring. Isomorphism theorems are examined by quotient rings. Finally, some algebraic properties are investigated by defining soft intersection maximal k-ideals.

Bipolar Spherical Fuzzy Soft Topology with Applications to Multi-Criteria Group Decision-Making in Buildings Risk Assessment

A generalized soft set model that is more accurate, useful, and realistic is the bipolar spherical fuzzy soft set (BSFSs). It is a more developed variant of current fuzzy soft set models that may be applied to characterize erroneous data in practical applications. Bipolar spherical fuzzy soft sets and bipolar spherical fuzzy soft topology are novel ideas that are intended to be introduced in this work. Bipolar spherical fuzzy soft intersection, bipolar spherical fuzzy soft null set, spherical fuzzy soft absolute set, and other operations on bipolar spherical fuzzy soft sets are some of the fundamental ideas defined in this work. The bipolar spherical fuzzy soft open set, the bipolar spherical fuzzy soft close set, the bipolar spherical fuzzy soft closure, and the spherical fuzzy soft interior are also defined. Additionally, the characteristics of this specified set are covered and described using pertinent instances. The innovative notion of BSFSs makes it easier to describe the symmetry of two or more objects. Moreover, a group decision-making algorithm based on the TOPSIS (Technique of Order Preference by Similarity to an Ideal Solution) approach to problem-solving is described. We analyze the symmetry of the optimal decision and ranking of feasible alternatives. A numerical example is used to show how the suggested approach may be used. The extensive benefits of the proposed work over the existing techniques have been listed.

Analysis of semigroups with soft intersection ideals

Abstract In this paper, semisimple semigroups, duo semigroups, right (left) zero semigroups, right (left) simple semigroups, semilattice of left (right) simple semigroups, semilattice of left (right) groups and semilattice of groups are characterized in terms of soft intersection semigroups, soft intersection ideals of semigroups. Moreover, soft normal semigroups are defined and some characterizations of semigroups with soft normality are given.

Two Different Types of Soft Near-Fields

Molodtsov’s soft set is a novel mathematical approach to address models containing uncertainty. The algebraic structures of this set approach are prominent issues. The main objective of this paper is to contribute algebraic structures in the soft set theory. Relatedly, the notions of soft intersection near-field and soft union near-field, and their fundamental properties are introduced. Also, some findings and results related to the emerging soft algebraic structures are included.

On Near-Rings with Soft Union Ideals and Applications

In this paper, we define soft union near-ring on a soft set by using soft sets, inclusion relation and union of sets. This new notion functions as a bridge among soft set theory, set theory and near-ring theory. We then derive its basic properties and investigate the relationship between soft intersection near-ring and soft union near-ring. Furthermore, we obtain some analog of classical near-ring theoretic concepts for soft union near-ring and give the applications of soft union near-ring to near-ring theory.

Soft Rω-Open Sets and the Soft Topology of Soft δω-Open Sets

The author devotes this paper to defining a new class of soft open sets, namely soft Rω-open sets, and investigating their main features. With the help of examples, we show that the class of soft Rω-open sets lies strictly between the classes of soft regular open sets and soft open sets. We show that soft Rω-open subsets of a soft locally countable soft topological space coincide with the soft open sets. Moreover, we show that soft Rω-open subsets of a soft anti-locally countable coincide with the soft regular open sets. Moreover, we show that the class of soft Rω-open sets is closed under finite soft intersection, and as a conclusion, we show that this class forms a soft base for some soft topology. In addition, we define the soft δω-closure operator as a new operator in soft topological spaces. Moreover, via the soft δω-closure operator, we introduce soft δω-open sets as a new class of soft open sets which form a soft topology. Moreover, we study the correspondence between soft δω-open in soft topological spaces and δω-open in topological spaces.

Unifying Classification and Bounding Box Regression Head For Object Detection

Object detection usually includes two parts: objection classification and location. At present, the popular object detectors usually use two detection heads: one head is used to predict classification score, and the other one is used to predict the bounding box (bbox), respectively. In this paper, we first stack classification head after feature extract convolutional neural networks of bbox regression head. Then, we establish the classification networks by using a bounding box feature. The bounding box feature is very useful when the classification head uses soft Intersection over Union (IoU) labels. In experiment parts, only using PASCAL VOC 2007 datasets, soft Centerness labels, and soft IoU labels get 50.06 mAP and 52.08 mAP on VOC 2007 test. Compared with FCOS, they have 1.08% and 1.12% improvements. Using PASCAL VOC 2007 and 2012 datasets, our Union A*B head gets 78.71mAP after 12 epochs training with ResNet-101 as backbone and FPN as the neck. Extensive experimental results show that the proposed algorithm is superior to other detection methods.

On Soft Intersection Leibniz Algebras

The main goal of this study is to introduce the description of soft Leibniz subalgebras (respectively soft Leibniz ideals) and to state some properties. Moreover, in this note, we investigate the concept of soft intersection Leibniz subalgebras (respectively soft intersection Leibniz ideals).

T-soft equality relation

The desire of generalizing some set-theoretic properties to the soft set theory motivated many researchers to define various types of soft operators. For example, they redefined the complement of a soft set, and soft union and intersection between two soft sets in a way that satisfies De Morgan's laws. In this paper, we introduce and study the concepts of $T$-soft subset and $T$-soft equality relations. Then, we utilize them to define the concepts of $T$-soft union and $T$-soft intersection for arbitrary family of soft sets. By $T$-soft union, we successfully keep some classical properties via soft set theory. We conclude this work by giving and investigating new types of soft linear equations with respect to some soft equality relations. Illustrative examples are provided to elucidate main obtained results.

Automated detection of defects with low semantic information in X-ray images based on deep learning

Nondestructive testing using X-ray imaging has been widely adopted in the defect detection of casting parts for quality management. Deep learning has been proved to be an effective way to detect defects in X-ray images. In this work, Feature Pyramid Network (FPN) which has been utilized broadly in many applications is adopted as our baseline. In FPN, there mainly exits two issues: firstly, down sampling operation in Convolutional Neural Network is often utilized to enhance the perception field, causing the loss of location information in feature maps, and secondly, there exists feature imbalance in feature maps and proposals. DetNet and Path Aggregation Network are adopted to solve the two shortages. To further improve the recall rate, soft Non-Maximum Suppression (soft-NMS) is adopted to remain more proposals that have high classification confidence. Defects in X-ray images of casting parts are provided with low semantic information, causing the different instances between detection results and annotations in the same area. We propose soft Intersection Over Union (soft-IOU) criterion which could evaluate several results or ground truths in the near area, making it more accurate to evaluate detection results. The experimental results demonstrate that the three proposed strategies have better performance than the baseline for our dataset.

Soft Intersection Nearsemirings and Its Algebraic Applications

In this manuscript, we introduce soft int-nearsemirings by utilizing the intersection operation of sets. We study the set theoretic characteristics of nearsemirings with the effects of soft set intersection operations. Soft int sub-nearsemirings, soft int-ideals ( $$SI$$ -ideals), soft int- $$c$$ -ideals ( $$SI{-}c$$ -ideals) are also introduced and discussed. We inter-relate the characteristics of nearsemirings and $$SI$$ -nearsemirings by applying different types of soft set product operations. Finally, we present few structural characteristics of $$SI$$ -ideals and $$SI{-}c$$ -ideals.

Characterizations of soft $$\varGamma $$-hyperideals in ordered $$\varGamma $$-semihypergroups

In this paper, soft intersection $$\varGamma $$ -hyperideals of ordered $$\varGamma $$ -semihypergroups over an initial universe $$\mathcal {V}$$ are defined and some properties of them with soft intersection product are obtained. Further, some characterizations of regular and intra-regular ordered $$\varGamma $$ -semihypergroups in terms of soft intersection $$\varGamma $$ -hyperideals are provided. We also introduce the notion of semisimple ordered $$\varGamma $$ -semihypergroups. Finally, we give some characterizations of semisimple ordered $$\varGamma $$ -semihypergroups in terms of soft prime and soft semiprime $$\varGamma $$ -hyperideals.

A soft set theoretic approach to an AG-groupoid via ideal theory with applications

In this paper, we study the structural properties of a non-associative algebraic structure called an AG-groupoid by using soft set theory. We characterize a right regular class of an AG-groupoid in terms of soft intersection ideals and provide counter examples to discuss the converse part of various problems. We also characterize a weakly regular class of an AG***-groupoid by using generated ideals and soft intersection ideals. We investigate the relationship between SI-left-ideal, SI-right-ideal, SI-two-sided-ideal, and SI-interior-ideal of an AG-groupoid over a universe set by providing some practical examples.