Closure Operator Research Articles

Basic concepts of complete residuated lattice-valued fuzzy mathematical morphology

The aim of this paper is to present basic concepts of lattice-valued fuzzy mathematical morphology. We use a complete residuated lattice as the codomain of fuzzy sets, a pair of fuzzy powerset operators, called the fuzzy erosion operator and the fuzzy dilation operator, is defined and their properties and relationships are studied. The pair of two operators forms a Galois adjunction and so that the induced fuzzy opening operator and fuzzy closing are an interior operator and a closure operator respectively. It is shown that the dilation stable sets and the erosion stable sets are equivalent, which form a fuzzy Alexandrov topology.

Neutrosophic SuperHyper Bi-Topological Spaces: Extra Topics

This manuscript holds the integral concepts presented by the previously published article called (Neutrosophic SuperHyper Bi-Topological Spaces). This essay contains new definitions related to the notion of SuperHyper Bi-Topological Spaces, such as SuperHyper Supra closure operator, the pairwise neutrosophic interior of the power set Pn1(x), three cascade numerical examples demonstrate the NSHBI-TS, pairwise neutrosophic nth-power sets in (τ11ndpair, τ22ndpair,Pn(x)), as well as extra definitions, theorems, corollaries, and propositions.

Smallest quasi-transitive extensions

Quasi-transitivity is a weakening of transitivity that has some attractive features, such as the important role it plays in the context of path-independent choice. However, the property suffers from the shortcoming that it does not allow for the existence of a closure operator. This paper examines the question to what extent an alternative operator can be defined that may then be used to ameliorate some of the limitations of quasi-transitivity imposed by the absence of a well-defined closure. To do so, we define the concept of a smallest quasi-transitive extension. A novel weakening of quasi-transitivity turns out to be necessary and sufficient for the existence of such a smallest extension. As an illustration, we apply the notion of a smallest quasi-transitive extension in the context of rational choice on arbitrary domains.

Use of surgical procedure manager to standardise operation steps and monitor surgeon performance in open repair of inguinal hernia

AbstractObjectivesTo study the feasibility of using surgical procedure manager (SPM), a digital checklist platform, to standardise surgical steps of open hernia repair and monitor the operative performance.MethodologyA retrospective study on all open mesh repair of inguinal hernia under local anaesthesia from September 2019 to November 2021 at the Prince of Wales Hospital was performed. The operative outcomes of patients having operations with or without the use of SPM were compared. Procedures using SPM had operation steps shown as a digital checklist inside the theatre. The time used for each surgical step was recorded and analysed. The operative performance of the surgeons was analysed by observing the trend of the mean operation time over time.ResultsA total of 123 patients were recruited, of which 52 were using the SPM. The median age of patients was 75 (range 49–93) years. A decreasing trend in the mean operation time for dissection, mesh placement, wound closure and total operation time was observed in surgeries using SPM. There was no significant difference in the operation time, theatre time, total length of stay, blood loss and readmission rate between the SPM and non‐SPM groups. The proportion of basic surgical trainees as coached surgeons in the SPM group was significantly higher (SPM = 52% vs non‐SPM = 28%, P = .07).ConclusionsThe use of SPM did not significantly prolong the operation time and produce comparable operative outcomes in open hernia repair. It provided the additional advantage of standardising operation steps and monitoring the performance of surgical trainees during their training.

Algebraic Recognition Approach in IoT Ecosystem

The solution to the problem of identifying objects in the IoT ecosystem of the Aral region is analyzed. The problem of constructing a correct algorithm with linear closure operators of a model for calculating estimates for identifying objects in the IoT ecosystem of the Aral region is considered. An algorithm operator is developed, which is considered correct for the problem Z, is the sum of q operators of the assessment calculation model, and is described by a set of numerical parameters 3·n·m·q, where n is the number of specified features, m is the number of reference objects, and q is the set of recognized objects. Within the framework of the algebraic approach, several variants of linear combinations of recognition operators are constructed, the use of which gives the correct answer on the control material, and this is proven in the form of theorems. The constructed correct recognition algorithms, which are the easiest to use, where there is no optimization procedure, make it possible to quickly solve the issue of identifying incoming information flows in the IoT ecosystem of the Aral region.

Predictive Value of Post-operative Cardiac Troponin I and Lactate Levels After Ventricular Septal Defect Closure

Objectives: Although the mortality rate of primary ventricular septal defect (VSD) closure surgery has been reduced to <0.5% in many centers, low cardiac output syndrome and multi-organ failure syndrome development in the post-operative period are still the most common causes of mortality and morbidity. The use of biochemical markers in the early period can be used as effective predictors for reducing mortality and morbidity. In this study, the effect of post-operative serum lactate and cardiac troponin I (cTNI) levels on hospital mortality in patients who underwent primary closure of VSD was investigated retrospectively. Methods: The effect of lactate and cTNI values on hospital mortality in 52 patients who underwent surgical repair for VSD was investigated. Serum lactate levels of all patients in the first 6 h after the operation; on the first post-operative day, cTNI values were examined retrospectively. Serum lactate levels exceeding 3.5 mmol/ lt and cTNI values exceeding 35 ng/mL were determined as the cut-off points. Results: Serum lactate level and cTNI increase were found to be statistically different in the mortality group (p<0.05). It was shown that increased cTNI was associated with weight, left ventricular end-diastolic diameter, and cardiopulmonary bypass time (p<0.05). Serum lactate levels were 4.1±0.5 mmol/lt in the non-mortality group and 15.3±8.3 mmol/lt in the mortality group, and the difference was statistically significant (p<0.05). Hospital mortality was observed in 6 patients. Conclusion: In patients undergoing VSD closure surgery, serum lactate levels measured in the first 6 h postoperatively and cTNI levels measured on the first post-operative day are associated with hospital mortality. Concomitant elevations of lactate and cTNI values in patients after VSD closure should suggest to take caution and early supportive treatments to reduce mortality.

Plastic Surgery Involvement With Surgical Management of Infected Ventricular Assist Devices Decreased Lifetime Return to Operating Room and 90-Day Infectious Complications.

The use of left ventricular assist devices (LVADs) for patients with end-stage cardiac failure awaiting heart transplantation has become increasingly common. However, ventricular assist device-related infections remain a major problem complicating their long-term use. Retrospective review has previously shown a decrease in lifetime return to operating room (RTOR) with no change in 90-day complications when a muscle or omental flap is used for coverage after washout for infection. We wished to determine if early plastic surgery intervention led to a decreased length of stay for these patients. Patients with LVAD readmitted for LVAD infection at a single institution from 2008 to 2021 were identified using a preexisting database. Patients were followed retrospectively for an average of 3.2 years. Patient demographics, preoperative diagnosis/disease state, type of ventricular assist device inserted, postoperative day of ventricular assist device infection onset, definitive device coverage, timing of coverage procedure after the initial washout for infection, type of flap used for coverage, 90-day complications after definitive coverage, and lifetime return to operating room for infection were reviewed. Comparison analysis with χ2 and analysis of variance testing was used to analyze outcomes. Of 568 patients admitted with an LVAD infection, 104 underwent operative debridement and closure by plastic and reconstructive surgery (PRS) or cardiothoracic surgery (CTS). Fifty-three underwent PRS closure, and 51 underwent CTS closure. There was an increased incidence of diabetes among the PRS group (P < 0.001); otherwise, there was no difference in baseline characteristics. There was increased RTOR over a lifetime with CTS closure compared with PRS (P = 0.03) and increased 90-day risk of infection (P = 0.007). Patients with PRS closure had an increased risk of postoperative hematoma (P = 046). Plastic and reconstructive surgery was typically consulted on hospital day 10. Both PRS and CTS closure patients were discharged on postoperative day 7, on average (P = 0.542). Plastic surgery involvement with surgical decision making and closure of infected LVAD devices has a decrease in lifetime RTOR and decreased 90-day complications related to infections. There may be a benefit to earlier PRS consultation for coverage assessment.

Efficacy of modified vacuum-assisted dressing versus conventional betadine dressing in wound healing of open fractures

AimThis study aimed to compare the effectiveness of a customized vacuum-assisted dressing to traditional betadine dressings for wounds in open fractures. Materials and methodsIn this prospective comparative study, 30 patients from two groups—group A receiving V.A.C. while group B receiving traditional dressing—were given data from sixty participants with open fractures. Wound was evaluated on days 0, 3, 7, 11, and 15 of the study. ResultsIn group A, there was a statistically significant decrease in the mean dimension of the wound overall (15.66 mm vs. 7.4 mm in group B), and it took an average of 9.83 days for healthy granulation tissue to emerge. In contrast to the 21 patients who had split skin grafting, five patients needed a flap as a final closure surgery. In group B, it took an average of 17 days for healthy granulation tissue to emerge. The authors used split skin grafting to close the wounds in 18 patients, and the wound was allowed to heal by secondary intention in 8 patients, while the flap was used in 4 patients. ConclusionOn comparing the modified Vacuum-assisted dressing to the standard dressing, there was considerable wound contraction and accelerated healing. Therefore, the authors observed that vacuum-assisted dressing treatment is superior to traditional betadine dressing in open fractures.

Театр как «наблюдение второго порядка»: опыт Никласа Лумана

The article describes a viewpoint on theatre arts from the perspective of the Systems theory developed by the social philosopher Niklas Luhmann. The target of the study is theatre as a part of the social system. The theatre, being extremely dialogical and “demonstrative” kind of art, is described in terms of communication: self-reference, hetero-reference, autopoiesis, operational closure, first-and second-order observation. The paper aims to consider the theatre as a subsystem of the social system “art”, focusing on the notion of “second-order observation” which presumably can be a key to understanding the contemporary theatre form. Despite its social significance theatre has rarely been an object of social and philosophical studies. One of the aims of this article is to attempt to fill this gap. Luhmann avoided the political bias which was not always possible for social philosophers of the mid-twentieth century, so his view on the space and structure of theatre may also be of interest to contemporary researchers.

On Soft Bitopological Ordered Spaces

On Soft Bitopological Ordered Spaces

The Ginsburg–Sands theorem and computability theory

The Ginsburg–Sands theorem from topology states that every infinite topological space has an infinite subspace homeomorphic to exactly one of the following five topologies on ω: indiscrete, discrete, initial segment, final segment, and cofinite. The original proof is nonconstructive, and features an interesting application of Ramsey's theorem for pairs (RT22). We analyze this principle in computability theory and reverse mathematics, using Dorais's formalization of CSC spaces. Among our results are that the Ginsburg–Sands theorem for CSC spaces is equivalent to ACA0, while for Hausdorff spaces it is provable in RCA0. Furthermore, if we enrich a CSC space by adding the closure operator on points, then the Ginsburg–Sands theorem turns out to be equivalent to the chain/antichain principle (CAC). The most surprising case is that of the Ginsburg–Sands theorem restricted to T1 spaces. Here, we show that the principle lies strictly between ACA0 and RT22, yielding arguably the first natural theorem from outside logic to occupy this interval. As part of our analysis of the T1 case we introduce a new class of purely combinatorial principles below ACA0 and not implied by RT22 which form a hierarchy generalizing the stable Ramsey's theorem for pairs (SRT22). We show that one of these, the Σ20 subset principle (Σ20-Subset), has the property that it, together with the cohesive principle (COH), is equivalent over RCA0 to the Ginsburg–Sands theorem for T1 CSC spaces.

Some new open sets in bipolar N-neutrosophic supra topological spaces

The primary focus of this work is to develop the concept of bipolar N-neutrosophic supra topological spaces. Also, extended some concepts such as closure and interior operators of N-neutrosophic supra topological spaces to Bipolar N-neutrosophic supra topological spaces. The properties and relationship between weak forms of bipolar N-neutrosophic supra topological open sets are also established. Further, suggested several separations amongst bipolar N-neutrosophic supra sets. Some distance between bipolar N-neutrosophic sets is introduced and an efficient approachfor group multi-criteria decision making based on bipolar N-neutrosophic sets is proposed.

Closure Operations on Intuitionistic Linear Algebras

Abstract In this paper, we introduce the notions of radical filters and extended filters of Intuitionistic Linear algebras (IL-algebras for short) and give some of their properties. The notion of closure operation on an IL-algebra is also introduced as well as the study of some of their main properties. The radical of filters and extended filters are examples of closure operations among several others provided. The class of stable closure operations on an IL-algebra L is used to study the unifying properties of some subclasses of the lattice of filters of L. In particular, we obtain that for a stable closure operation c on an IL-algebra, the collection of c-closed elements of its lattice of filters forms a complete Heyting algebra. Hyperarchimedean IL-algebras are also characterized using closure operations. It is shown that the image of a semi-prime closure operation on an IL-algebra is isomorphic to a quotient IL-algebra. Some properties of the quotients induced by closure operations on an IL-algebra are explored.

Closure operators constructed by logical operations on bounded lattices

In this paper, closure operators obtained from functions having some properties on bounded lattices are defined. By this way, it is aimed to generalize the notions T and U-closure operators obtained from t-norms and uninorms, respectively. The relationships between the closure operators obtained from functions and their conjugacies (dual functions) are determined. In special cases, the closure operators from implications making closure operators from R-, (S,N)-, QL- implications are determined. Also, the closures of the sets according to the closure operators from implications are studied. The orders obtained from closure operators are introduced, and the properties are discussed.

Autonomous robotic valve turning: a visual-guided approach based on deep learning

Background With the advancement of robot technology, firefighting robots are increasingly utilized for environmental reconnaissance, detection, and rescue operations, showcasing significant advantages. Visual recognition and localization serve as crucial foundations for robots to efficiently accomplish predefined tasks. Methods In this article, a control method for firefighting robot valve operations based on the YOLO v5 target detection algorithm is proposed. This strategy solves the issue of low accuracy and efficiency in valve closure operations during hazardous gas or liquid leaks. By employing a collected dataset of valve images and leveraging deep learning-based target detection methods, the YOLO v5 network is trained and tested to enhance valve recognition accuracy and speed. The proposed approach is further validated through simulations on the Webots platform, where a mobile robot is controlled based on visual guidance to perform valve closure tasks in a simulated hazardous environment. Results The valve recognition based on YOLO v5 achieves an accuracy of 82.36%, a recall rate of 94.82%, and a mean Average Precision of 90.74%. In the Webots simulation, the robotic system accurately identifies and locates valves, smoothly rotates and tightens them, and subsequently retrieves the mechanical arm. The simulation results demonstrate the effectiveness of the proposed strategy. Conclusions The valve recognition strategy presented in this article has important implications for fire fighting robots to close valves and aid in disaster relief, particularly in harsh environments.

A Novel Constructing Continuous and Topology Approach to Fuzzy β-covering

Fuzzy β-covering(Fβ-C) plays a key role in processing real-valued data sets and covering plays an important role in the topological spaces. Thus they have attracted much attention. But the relationship between Fβ-C and topology has not been studied. This inspires the research of Fβ-C from the perspective of topology. In this paper, we construct Fβ-C rough continuous and homeomorphism mappings by using Fβ-C operator. We not only obtain some equivalent descriptions of the mappings but also profoundly reveal the relationship of two Fβ-C approximation spaces. We give the classification method of Fβ-C approximation spaces with the help of homeomorphism mapping, propose a new method to construct topology induced by Fβ-C operator and investigate the properties in the topological spaces further. Finally, we obtain the necessary and sufficient conditions for Fβ-C operators to be topological closure operators.

Single-Valued Neutrosophic Roughness via Ideals

In this paper, we connect the idea of single-valued neutrosophic ideal to the concept of single-valued neutrosophic approximation space to define the concept of single-valued neutrosophic ideal approximation spaces. We present the single-valued neutrosophic ideal approximation interior operator intψΦ and the single-valued neutrosophic ideal approximation closure operator clψΦ, and we present the single-valued neutrosophic ideal approximation preinterior operator pintψΦ and the single-valued neutrosophic ideal approximation pre-closure operator pclψΦ about this concerning single-valued neutrosophic ideal defined on the single-valued neutrosophic approximation space (χ˜,ϕ) related with some single-valued neutrosophic set ψ∈ξχ˜. Also, we present single-valued neutrosophic separation axioms, single-valued neutrosophic connectedness, and single-valued neutrosophic compactness in single-valued neutrosophic approximation spaces and single-valued neutrosophic ideal approximation spaces as well, and prove the associations in between.

A CALCULATION OF THE PERFECTOIDIZATION OF SEMIPERFECTOID RINGS

AbstractWe show that perfectoidization can be (almost) calculated by using p-root closure in certain cases, including the semiperfectoid case. To do this, we focus on the universality of perfectoidizations and uniform completions, as well as the p-root closed property of integral perfectoid rings. Through this calculation, we establish a connection between a classical closure operation “p-root closure” used by Roberts in mixed characteristic commutative algebra and a more recent concept of “perfectoidization” introduced by Bhatt and Scholze in their theory of prismatic cohomology.

Special Discrete Fuzzy Numbers on Countable Sets and Their Applications

There are some drawbacks to arithmetic and logic operations of general discrete fuzzy numbers, which limit their application. For example, the result of the addition operation of general discrete fuzzy numbers defined by the Zadeh’s extension principle may not satisfy the condition of becoming a discrete fuzzy number. In order to solve these problems, special discrete fuzzy numbers on countable sets are investigated in this paper. Since the representation theorem of fuzzy numbers is the basic tool of fuzzy analysis, two kinds of representation theorems of special discrete fuzzy numbers on countable sets are studied first. Then, the metrics of special discrete fuzzy numbers on countable sets are defined, and the relationship between these metrics and the uniform Hausdorff metric (i.e., supremum metric) of general fuzzy numbers is discussed. In addition, the triangular norm and triangular conorm operations (t-norm and t-conorm for short) of special discrete fuzzy numbers on countable sets are presented, and the properties of these two operators are proven. We also prove that these two operators satisfy the basic conditions for closure of operation and present some examples. Finally, the applications of special discrete fuzzy numbers on countable sets in image fusion and aggregation of subjective evaluation are proposed.

Predisposing Factors for Postoperative Complications in the Year Following Fronto-Orbital Advancement and Remodeling: A Single Institution Study of 267 Patients.

Fronto-orbital advancement and remodeling (FOAR) is a common surgical approach used for craniosynostosis conferring functional and aesthetic benefit. There are few reports examining predisposing factors for postoperative complications within the first year after surgery. This study aimed to establish complication rates and identify risk factors for inferior outcomes in a large population of patients undergoing FOAR. All patients who underwent fronto-orbital advancement and remodeling from 2013-2022 at our institution were retrospectively studied. Perioperative and postoperative data were collected to yield outcomes analyses. Multivariable logistic regression with backwards selection was performed to identify predictors of postoperative complications. 267 patients underwent FOAR. The overall complication rate was 14.2%, most commonly delayed wound healing (7.4%), postoperative blood transfusion (5.8%), and infection requiring readmission (1.9%). Tense closure independently predicted delayed wound healing (p<0.001) and infection requiring readmission (p=0.03). Syndromic patients were more likely than non-syndromic children to have undergone prior craniofacial surgery (45.3% vs 23.8%, p=0.003). Syndromic status and prior craniofacial surgery were associated with increased risk of developing infection requiring readmission (p=0.012 and p=0.004, respectively). A greater proportion of malnourished patients experienced postoperative complications compared to patients without malnourishment (24.4% vs 12.1%, p=0.031), though there were no significant differences in individual postoperative outcomes. Identified risk factors for complications included syndromic status, tense closure, and prior craniofacial surgery. Most complications were managed nonoperatively. These factors may be considered in preoperative planning and when counseling patient families.