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In this paper, we determine the fuzzy similarity measures of the U. S. state rankings with respect to domestic violence, female homicide, and sexual violence against teens. We find that the fuzzy similarity measures are low. We then consider the best state rankings and determine the fuzzy similarity measures of this ranking a with the previous three rankings. We also develop some theoretical results concerning fuzzy similarity measures.

5G New Radio (NR), introduced in 2019 in the 3rd Generation Partnership Project (3GPP) Release 15, has become the global radio standard for 5G networks. Because of the presence of an increasing number of available 5G gNodeBs (gNBs), HandOver (HO) management is crucial, especially in terms of Quality of Service (QoS) and Quality of Experience (QoE) perceived by a User Equipment (UE). Unnecessary HandOvers (UHOs) cause latency peaks (on the order hundreds of milliseconds) and multiple throughput drops in 5G communications. In this paper, we first carry out an experimental campaign to investigate the behaviour of latency and throughput in correspondence to UHOs. Then, on the basis of a Matlab-based 5G NR DownLink (DL) transmission simulator, we propose an innovative linear regression-based algorithm to avoid UHOs, which relies on Channel State Information-Reference Signal Received Power (CSI-RSRP) measurements.

The United Nation's Sustainable Development Goals encourage countries to solve many social problems‎. ‎One of these problems is homelessness‎. ‎We consider those goals which are most pertinent to homelessness according to \cite{13}‎. ‎We rank countries with respect to the‎ achievement of these goals‎. ‎We use fuzzy similarity measures to determine‎ ‎ the degree of similarity between these rankings‎. ‎We use three methods to‎ ‎ rank the counties‎, ‎namely‎, ‎the Analytic Hierarchy Process‎, ‎the Guiasu‎ ‎ method,‎ ‎and the Yen method‎. ‎Overall scores of categories in some basic‎ ‎ research papers pertaining to Sustainable Development Goals were obtained by‎ ‎ using multiplication of the scores of the category's targets‎. ‎Multiplication‎ ‎ was used to agree with the philosophy that in order for a high score to be‎ ‎ obtained,‎ ‎all targets must have a high score‎. ‎To support this philosophy in‎ ‎ the decision process‎, ‎we use the $t$-norms bounded difference‎, ‎algebraic‎ ‎ product,‎ ‎and standard intersection as experts‎. ‎We also suggest a way the‎ ‎ techniques used here can be extended to nonstandard analysis‎.

The Aichi biodiversity targets were established by the UN convention of biological Diversity and consist of 20 specific targets to address and mitigate biodiversity loss across the globe. We determine how well OECD countries are achieving the Aichi targets. We use the Sustainable Development Goals to make the determination. The Biodiversity and Habitat issue category assesses countries’ actions toward retaining natural ecosystems and protecting the full range of biodiversity within their borders. It consists of seven indicators: terrestorial biome protection (weighted for national and global rarity of biomes), marine protected areas, Protected Areas Representativeness Index, Species Habitat Index, Species Protection Index, and Biodiversiy Index, [4]. We determine the similarity between the rankings determined by the weighted average values and the Environmental Performance Index (EPI) scores.

It has been shown in literature that in the two-dimensional case, the lattices of truth values considered are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy sets. In this paper, we show that there is a strong connection between weighted graphs and fuzzy graphs. We accomplish this by using lattice isomorphisms. Consequently, under certain conditions, results for one area can be carried over immediately to the other. Many situations in fuzzy graph theory do not depend on the weights of the vertices. The situation of providing weights for the vertices of a weighted graph is also considered. We also consider lattice homomorphisms with an illustration involving nonstandard analysis. In particular, we consider a nonstandard weighted graph, i.e., a graph where the weights of the edges are from a nonstandard interval.

In this paper‎, ‎we extend the fuzzy similarity measure of‎ ‎two rankings to any finite number of rankings‎. ‎We provide a method to‎ ‎convert a measure for a finite number of rankings to a number that‎ ‎represents the number for two rankings‎. ‎We apply our results to the‎ ‎sustainability ranking of countries by the Environmental Performance Index‎ ‎(EPI)‎. ‎The $2020$ EPI provides a summary of the state of sustainability‎ ‎around the world‎. ‎It uses $32$ performance indicators across $11$‎ ‎categories‎. ‎These indicators provide a way to determine problems‎, ‎set‎ ‎targets‎, ‎track trends‎, ‎understand outcomes‎, ‎and identify best policy‎ ‎practices‎. ‎The EPI ranks $180$ countries on environmental health and‎ ‎ecosystem vitality‎. ‎The EPI provides a method in support of efforts to meet‎ ‎the targets of the UN Sustainable Development Goals‎. ‎The EPI determined‎ ‎that the Global West region ranked the highest‎. ‎The purpose of our project‎ ‎is to find the similarity of the $11$ rankings of the countries for eight‎ ‎different regions‎.

In this paper, we extend some results of nonstandard analysis to include concepts from fuzzy mathematics. Then we apply our results to issues from special and general relativity and the theory of light-clocks. The extension includes concepts of fuzzy numbers, continuity, and differentiability. Our goal is to provide a new research area in fuzzy mathematics.

Introduction: Blood pressure (BP) measurement frequently guides management in critical care. Direct readings from a major artery is considered the gold standard. However, intra-arterial cannulation is associated with many risks. Hence, alternative noninvasive BP (NIBP) measurements are used for prolonged monitoring of BP among critically ill patients. Discrepancies between intra-arterial BP (IABP) and NIBP measurement can adversely affect therapeutic decisions and may have a negative impact of outcomes. Objectives: To compare upper limb and lower limb BP measured by auscultatory and oscillometric methods with IABP (by arterial cannulation) in hemodynamically unstable patients. Materials and Methods: Patients in the medical intensive care unit of Pushpagiri Institute of Medical Science and Research Centre were included over 24 months (50 patients admitted) in the clinical cross-sectional study. All patients who had a systolic BP (SBP) below 100 mmHg with an intra-arterial line were included under the study after obtaining an informed consent from the patient/patient's bystander. The study design was approved by the Ethics Committee at Pushpagiri Institute of Medical Science and Research Centre. Choice of cuff size was made based on the limb circumference (midarm and midcalf) and manufacturer guidelines. BP was measured in arm using a welch allyn aneroid manometer. Oscillometric NIBP was relied on an MP20 model (Philips Medical Systems) connected to the nondisposable, reusable cuff. The intra-arterial catheter was connected through a pressure transducer to the monitor (Philips). With the patient supine, the pressure transducer was zeroed at the level of the mid-axillary line and the correct shape of the arterial pressure waveform was ascertained. Measurements: BP was measured at 0 h, 3 h and once the patient becomes hemodynamically stable using auscultatory, oscillometric, and IABP at arm and calf, respectively. Quantitative variables were expressed as mean standard deviation, whereas categorical variables were expressed as frequency (%). Karl Pearson's Correlation Coefficient was used to find our relationship of BP measured by two different methods with BP measured using arterial cannulation. P < 0.05 was considered the threshold for statistical significance. Statistical analyses was performed using a Statistical Software Package SPSS version 20. Results: Out of 50 patients admitted in a hemodynamically unstable state, 68% were male and 32% were female. Male-to-female ratio was 2.125. The mean age of patients was 65.9 ± 12.2. Majority of the patients belonged to the age group 61–70 years (30%) and the least number of patients in age group

Acute upper airway obstruction, an emergent situation, can sometimes put the clinician in a dilemma with no positive history or clinical findings to aid in the diagnosis. A myriad of conditions causes upper airway obstruction. Priority is to secure the airway and then seek out the underlying cause. Computed tomography scan is an important imaging modality for reaching a definitive diagnosis and might at times, reveal unexpected findings. In this case series, authors report three cases of acute upper airway obstruction which were atypical manifestation of diseases. Case 1 (82-year-old male) is about Lemierre’s syndrome with compromised airway in the absence of abscess formation. Case 2 (47-year-old male) depicts an atypical presentation of Boerhaave syndrome as retropharyngeal accumulation of air and pneumomediastinum. Case 3 (67-year-old male) is about retropharyngeal haematoma in a patient with anticoagulant therapy without any definite history of trauma. Treatment with reversal of anticoagulation was successful in the case 3. It is important for the clinician to be aware of the unusual reasons for airway compromise, as early suspicion can translate into better patient survival. Airway should be secured by either intubation or tracheostomy. Many a time, radiological and blood investigations help to arrive at a definite diagnosis.

Abstract In this paper, we prove some fixed point theorems for ψF-contractions in the framework of quasi-metric spaces generalizing and improving several similar results in metric spaces. At the same time, we consider iterated function systems consisting of ψF-contractions on quasi-metric spaces, and we give some sufficient conditions for the existence and uniqueness of their attractor which is, generally, a fractal. Some illustrative examples are provided.

All sports come with a risk of injury, and in general, the more contact involved in the sports, the higher the risk of a more significant or traumatic injury. The most frequent types of sports injuries are sprains (ligament injuries), strains (muscle injuries), and stress fractures (bone injuries). In sports medicine, a catastrophic injury is defined as severe trauma to the human head, spine, or brain. Concussions in sports became a major issue in the 2000s as evidence connected repeated concussions and subconcussive hits with chronic traumatic encephalopathy and increased suicide risk. Overuse and repetitive stress injury problems associated with sports include jumper's knee, tennis elbow, and tendinosis. In this review article, we have made an attempt to describe the head to toe spectrum of sports-related injuries including traumatic injuries of the head and face, extremity injuries, soft-tissue injuries, and contact sports-related injuries.

Intervals and convexity play crucial roles in the applications of graph theory such as town planning and design of graphics. In this article, the concept of geodetic interval in graphs is extended to fuzzy graphs. Intervals are useful in the study of properties of fuzzy graphs which depend on the geodetic distance between vertices. The axiomatic definition of intervals in fuzzy graphs are used to define intervals in different fuzzy graph structures like fuzzy trees and complete fuzzy graphs. Finally a set theoretic operations of intervals like union, intersection are also discussed and some results are obtained.

Bronchopleural fistula (BPF) is a sinus tract between the bronchus and the pleural space that may result from a necrotizing pneumonia/empyema (anaerobic, pyogenic, tuberculous, or fungal), lung neoplasms, and blunt and penetrating lung injuries or may occur as a complication of procedures such as lung biopsy, chest tube drainage, thoracocentesis, or radiation therapy. The diagnosis and management of BPF remain a major therapeutic challenge for clinicians, and the lesion is associated with significant morbidity and mortality. Here, we present a 70-year-old male with acquired BPF due to chemical pneumonitis caused by aspiration of kerosene who presented with the symptoms of fever, cough with expectoration, breathlessness and signs of tachycardia, tachypnea, diminished breath sounds, and crepitations. After a 3-week course of culture-sensitive antibiotics with β-lactam and β-lactamase inhibitors, open drainage of the empyema was done following which the patient showed symptomatic improvement and was discharged.

Patients with inflammatory bowel disease (IBD) have a higher risk of venous thrombosis compared with the general population. The most common sites of venous thrombosis in IBD patients are the deep veins of the legs, pulmonary system, and portal and mesenteric veins. However, cerebral venous thrombosis (CVT) is rarely associated with IBD. In patients with IBD complicated by CVT, favorable outcomes are possible with early diagnosis and appropriate treatment. However, when patients are not treated, the mortality rate can be as high as 50%. Here, we present a 32-year-old man with the complaints of headache and seizures earlier diagnosed with ulcerative colitis. A diagnosis of CVT was made based on imaging findings. Thromboembolism is an extraintestinal complication of IBD, more frequently venous thrombosis and pulmonary thromboembolism.

In a fuzzy graph, the edges are mainly classified into α, β and δ. In this paper, some sequences in fuzzy graphs are introduced, whose concepts are based on the classification of edges. Besides, characterizations for blocks in fuzzy graphs and fuzzy trees are obtained. It is shown that β sequence of a fuzzy tree is a zero sequence and α sequence of a block is a binary sequence.

Graph models are fundamental in network theory. But normalization of weights are necessary to deal with large size networks like internet. Most of the research works available in the literature have been restricted to an algorithmic perspective alone. Not much have been studied theoretically on connectivity of normalized networks. Fuzzy graph theory answers to most of the problems in this area. Although the concept of connectivity in fuzzy graphs has been widely studied, one cannot find proper generalizations of connectivity parameters of unweighted graphs. Generalizations for some of the existing vertex and edge connectivity parameters in graphs are attempted in this article. New parameters are compared with the old ones and generalized values are calculated for some of the major classes like cycles and trees in fuzzy graphs. The existence of super fuzzy graphs with higher connectivity values are established for both old and new parameters. The new edge connectivity values for some wider classes of fuzzy graphs are also obtained. The generalizations bring substantial improvements in fuzzy graph clustering techniques and allow a smooth theoretical alignment. Apart from these, a new class of fuzzy graphs called generalized t-connected fuzzy graphs are studied. An algorithm for clustering the vertices of a fuzzy graph and an application related to human trafficking are also proposed.

In 2015, the leaders of all the UN’s Member States agreed to the 2030 Agenda for Sustainable Development. The 17 Sustainable Development Goals and their 169 associated targets address five areas of critical importance: people, planet, prosperity, peace, and partnership. The purpose of this paper is to take the metrics and data provided and transform them into a fuzzy logic setting. This allows for the analysis of the results in SDG Index and Dashboards Report 2019 by using the techniques of fuzzy logic. Many of these 17 Sustainable Development Goals are related to the terrible crime of human trafficking. We also examine these goals in a fuzzy logic setting.

The concepts of connectivity and cycle connectivity play an important role in fuzzy graph theory. In this article, cyclic cutvertices, cyclic bridges and cyclically balanced fuzzy graphs are discussed. It is proved that a vertex in a fuzzy graph is a cyclic cutvertex if and only if it is a common vertex of all strong cycles with maximum strength. Also a cyclic cutvertex cannot be a fuzzy endvertex in a fuzzy graph. A characterization of cyclically balanced fuzzy graphs is obtained. Cyclic vertex connectivity and cyclic edge connectivity of fuzzy graphs are also discussed.

Primary tuberculosis (TB) of the skull is a very rare entity scantily described in literature with 0.2%–1.3% of cases. The different radiological forms of calvarial TB described are - circumscribed lesions of the sclerotic and lytic type and diffuse TB of the cranium. Treatment for skull TB includes antituberculous therapy along with appropriate surgical intervention. Here, we present a case of calvarial TB presenting as multiple osteolytic soft tissue lesions.

It is the case that, in certain applications of fuzzy graphs, a t-norm, instead of a minimum, is more suitable. This requires the development of a new theory of fuzzy graphs involving an arbitrary t-norm in the basic definition of a fuzzy graph. There is very little known about this type of fuzzy graph. The purpose of this paper is to further develop this type of fuzzy graph. We concentrate on the relatively new concept of fuzzy incidence graphs.