In this paper, some statistical properties of the Choquet integral are discussed. As an interesting application of Choquet integral and fuzzy measures, we introduce a new class of exponential-like distributions related to monotone set functions, called , by combining the properties of Choquet integral with the exponential distribution. We show some famous statistical distributions such as gamma, logistic, exponential, Rayleigh and other distributions are a special class of Choquet distributions. Then, we show that this new proposed Choquet exponential distribution is better on daily gold price data analysis. Also, a real dataset of the daily number of new infected people to coronavirus in the USA in the period of 2020/02/29 to 2020/10/19 is analyzed. The method presented in this article opens a new horizon for future research.

Since the global COVID-19 outbreak in the spring of 2020, online instruction has replaced traditional classroom instruction as the main method of educating students. Teaching physical education online can be challenging, as it may be difficult to teach students certain movements, accurate student mobility, and appropriate exercise assignments. This paper proposed an online teaching support system with sustainable development features that utilize several large data sets. The system is based on the deep learning image recognition algorithm ResNet34, which can analyze and correct student actions in real-time for gymnastics, dance, basketball, and other sports. By combining the attention mechanism module with the original ResNet34, the detection precision of the system can be enhanced. The sustainability of the system is evident from the fact that the data set can be expanded in response to the emergence of new sports categories and can be kept current in real-time. According to experiments, the target identification accuracy of the proposed system, which combines ResNet34 and the attention mechanism, is higher than that of several other methods currently in use. The proposed techniques outperform the original ResNet34 in terms of accuracy, precision, and recall by 4.1%, 2.8%, and 3.6%, respectively. The suggested approach significantly improves student action correction in virtual sports instruction.

With the opening of the Stock Connect programs, the mainland China and Hong Kong stock markets are becoming more closely linked. In this paper, we develop a China's stock market risk early warning system. The proposed early warning system consists of three components. First, we use value at risk (VaR) to identify the stock market risk in which stock market risk is divided into multiple categories instead of two categories. Second, we construct a comprehensive indicator system in which basic indicators, technical indicators, overseas return rate indicators, and macroeconomic indicators are considered simultaneously. Third, we use four machine learning models, namely long short-term memory (LSTM), gate recurrent unit (GRU), multilayer perceptron (MLP), and EXtreme Gradient Boosting algorithm (XGBoost), to predict China's stock market risk. Experimental results show that: (1) Considering the macroeconomic indicators and basic indicators of Shanghai Composite Index (SSEC), ShenZhen Component Index (SZCZ) and Hang Seng Index (HSI) can significantly improve the performance of predicting China's stock market risk. (2) The opening of SH-HK Stock Connect program improves the predictive performance, but the opening of SZ-HK Stock Connect program decreases the predictive performance. (3) The indicators related to Hong Kong become more important after the SZ-HK Stock Connect program.

COVID-19 has created many complications in today's world. It has negatively impacted the lives of many people and emphasized the need for a better health system everywhere. COVID-19 is a life-threatening disease, and a high proportion of people have lost their lives due to this pandemic. This situation enables us to dig deeper into mortality records and find meaningful patterns to save many lives in future. Based on the article from the New Indian Express (published on January 19, 2021), a whopping 82% of people who died of COVID-19 in Tamil Nadu had comorbidities, while 63 percent of people who died of the disease were above the age of 60, as per data from the Health Department. The data, part of a presentation shown to Union Health Minister Harsh Vardhan, show that of the 12,200 deaths till January 7, as many as 10,118 patients had comorbidities, and 7613 were aged above 60. A total of 3924 people (32%) were aged between 41 and 60. Compared to the 1st wave of COVID-19, the 2nd wave had a high mortality rate. Therefore, it is important to find meaningful insights from the mortality records of COVID-19 patients to know the most vulnerable population and to decide on comprehensive treatment strategies.

Deep neural networks (DNN) effectiveness are contingent upon access to quality-labelled training datasets since label mistakes (label noise) in training datasets may significantly impair the accuracy of models trained on clean test data. The primary impediments to developing and using DNN models in the healthcare sector include the lack of sufficient label data. Labeling data by a domain expert are a costly and time-consuming task. To overcome this limitation, the proposed Multi-Tier Rank-based Semi-supervised deep learning (MTR-SDL) for Shoulder X-Ray Classification uses the small labelled dataset to generate a labelled dataset from unable dataset to obtain performance equivalent to approaches trained on the enormous dataset. The motivation behind the suggested model MTR-SDL approach is analogous to how physicians deal with unknown or suspicious patients in everyday life. Practitioners handle these questionable circumstances with the support of professional colleagues. Before initiating treatment, some patients consult with a range of skilled doctors. Patients are treated according to the most suitable professional diagnosis (vote count). In this article, we have proposed a new ensemble learning technique called "Rank based Ensemble Selection with machine learning models" (MTR-SDL) approach. In this technique, multiple machine learning models are trained on a labeled dataset, and their accuracy is ranked. A dynamic ensemble voting approach is then used to tag samples for each base model in the ensemble. The combination of these tags is used to generate a final tag for an unlabeled dataset. Our suggested MTR-SDL model has attained the best accuracy and specificity, sensitivity, precision, Matthew's correlation coefficient, false discovery rate, false positive rate, f1 score, negative predictive value, and false negative rate negative 92.776%, 97.376%, 86.932%, 96.192%, 85.644%, 3.808%, 2.624%, 91.072%, 90.85%, and 13.068% for unseen dataset, respectively. This approach has the potential to improve the performance of ensemble models by leveraging the strengths of multiple base models and selecting the most informative samples for each model. This study results in an improved Semi-supervised deep learning model that is more effective and precise.

[This retracts the article DOI: 10.1007/s00500-020-05503-5.].

The COVID-19 pandemic has had significant impacts on the health of individuals and communities around the world. While the immediate health impacts of the virus itself are well-known, there are also a number of post-pandemic health issues that have emerged as a result of the pandemic. The pandemic has caused increased levels of anxiety, depression, and other mental health issues among people of all ages. The isolation, uncertainty, and grief caused by the pandemic have taken a toll on people's mental well-being, and there is a growing concern that the long-term effects of the pandemic on mental health could be severe. Many people have delayed or avoided medical care during the pandemic, which could lead to long-term health problems. Additionally, people who have contracted COVID-19 may experience ongoing symptoms, such as fatigue, shortness of breath, and muscle weakness, which could impact their long-term health. Machine learning (ML) can be a powerful tool to analyze the health impact of the post-pandemic period. With the vast amounts of data available from electronic health records, public health databases, and other sources, this article is making use of ML methods which can help identify patterns and insights to conclude the study. The proposed ML models can analyze health data to identify trends and patterns that may indicate future health problems. By monitoring patterns in medical records and public health data, the proposed ML model can help public health officials detect and respond to outbreaks more quickly. The survey outcome reveals that the level of physical activities has been decreased by 22% during COVID-19-outbreak. The variance is shown at 49% during COVID-19 outbreak. The absence of physical activity (PA) and perceived stress (PS) are observed to be suggestively correlated with the QoL (quality of life) of adults. Deteriorated mental health also disrupts the normal lives and impacts the sleeping quality of people. The analysis of the data is performed using statistical analytical tools to depict the consequences of pandemic on the health of individuals aged between 50 to 80 years.

The evolution of a novel technique to handle multi-attribute decision-making (MADM) problems under interval-valued Fermatean fuzzy numbers is the main motivation of this paper. We aim to introduce several initiative aggregation operators (AOs), including Hamacher interactive weighted averaging, Hamacher interactive ordered weighted averaging, Hamacher interactive hybrid weighted averaging operations, etc., to acquire our desired outcomes. Then, the distinguished characteristics of these AOs are investigated. Furthermore, the suggested AOs are carried out to build a technique to MADM issues using interval-valued Fermatean fuzzy information. A case study of mine emergency plan selection is then narrated to elaborate the practicality and effectiveness of the developed method. The influence of parametric values on decision-making outcomes is investigated considering the distinct values of parameter. After discussing the developed work and seeing its applications, we come across with the conclusion that the dominant privilege of adaptation of the above-mentioned AOs is situated in the fact that these operators allow a progressively complete approach on the matters to decision-makers. Hence, the method recommended in this study offers progressively wide, enhanced accuracy and actual outcomes when compared with the prevailing associated strategies. Therefore, this technique plays a vital role in actual-life MADM problems.

With the recent focus on supply risk management in sustainable supply chains, it is more important than ever to evaluate and select the right sustainable suppliers from a supply risk perspective. However, few existing studies consider supply risks from the perspective of all three triple-bottom-line dimensions at the same time. To bridge this research gap, this research constructs a supply risk perspective integrated sustainable supplier selection model in the intuitionistic fuzzy environment. First of all, the weights of decision-makers in the decision-making group are obtained by intuitionistic fuzzy set. Secondly, after obtaining the aggregated intuitionistic fuzzy decision matrix considering the weight of decision-makers, the fuzzy entropy weight method is used to calculate criteria weight, objectively. Then, an improved failure mode and effects analysis is used to undertake risk assessments and to identify high-risk suppliers. Last but not least, the extended alternative queuing method is adopted to rank the eligible sustainable suppliers in the intuitionistic fuzzy environment. The proposed model not only reduces the uncertainty of decision-making in sustainable supplier selection, but also enables focal companies to reduce supply risk in their sustainable supplier selection practices and prevent the failure modes that relate to supply risk. The practicality and effectiveness of the proposed model are verified through an empirical illustration in a leading electrical appliance manufacturer in China.

[This retracts the article DOI: 10.1007/s00500-021-05948-2.].

In this paper, we describe an activity that involves economics and mathematics. It is included in the planning of orientation paths towards university studies within the Mathematical High School Project and is dedicated to students in the last years of high school. In particular, this research will deal with the issue of solving an economic problem using not only real analysis instruments but also geometrical topics concerning Euclidean geometry and topology. Mathematics becomes a language to understand and explain a real life problem, such as determining the optimal position of an airport, a nuclear reactor and so on. Some activities made use of dynamic geometry software and computer simulations.

[This retracts the article DOI: 10.1007/s00500-020-05451-0.].

At present, the quality of online video courses in China is mixed. There are several reasons for the quality of online video courses. 1. The advantages and disadvantages of the front-end video capture equipment itself; 2. The distance of online video transmission; 3. The medium through which the video is transmitted; 4. Watch whether there is relevant interference information in the signal where the video is located and whether the video is compressed during transmission. These reasons lead to that although there is much to learn in the video, the resolution is too low to see from the video. With the development of the current social environment, most of the courses need online teaching. Therefore, in order to improve some problems in video playing caused by the increase of online teaching amount caused by the current environment, this paper provides higher resolution video for online courses by using high-resolution image processing technology based on the elliptic partial differential equation online video course. The high resolution processing technology used in this paper is centered on filtering algorithm. On the basis of the existing online video course of elliptic partial differential equations, the use of high-resolution technology can overcome the resolution limit of the hardware itself and further improve the video quality of online video teaching.

Enhanced index tracking (EIT) problem is concerned with selecting a tracking portfolio to beat the benchmark on return while having the minimum tracking error. This paper addresses the EIT problem based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables. Under the framework of uncertainty theory, the paper proposes a new uncertain EIT model where the higher-order moment of the downside is used as the tracking error measure, as higher-order moment makes the model more widely applicable and the downside risk is in line with investors' perception of risk. Besides, some realistic constraints are considered in the new uncertain EIT model. Then, the properties of the proposed model are discussed. To solve the model, we proposed, which is a nonlinear integer programming problem, a meta-heuristic algorithm presented. The efficiency of the algorithm and the applications of the proposed model are illustrated through numerical experiments.

This article introduces the structure of the -regulated interval-valued neutrosophic soft set (abbr. -INSS). The structure of -INSS is shown to be capable of handling the sheer heterogeneity and complexity of real-life situations, i.e. multiple inputs with various natures (hence neutrosophic), uncertainties over the input strength (hence interval-valued), the existence of different opinions (hence soft), and the perception at different strictness levels (hence -regulated). Besides, a novel distance measure for the -INSS model is proposed, which is truthful to the nature of each of the three membership (truth, indeterminacy, falsity) values present in a neutrosophic system. Finally, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a (VIKOR) algorithm that works on the -INSS are introduced. The design of the proposed algorithms consists of TOPSIS and VIKOR frameworks that deploy a novel distance measure truthful to its intuitive meaning. The conventional method of TOPSIS and VIKOR will be generalized for the structure of -INSS. The parameters and in the -INSS model take the role of strictness in accepting a collection of data subject to the amount of mutually contradicting information present in that collection of data. The proposed algorithm will then be subjected to rigorous testing to justify its consistency with human intuition, using numerous examples which are specifically made to tally with the various human intuitions. Both the proposed algorithms are shown to be consistent with human intuitions through all the tests that were conducted. In comparison, all other works in the previous literature failed to comply with all the tests for consistency with human intuition. The -INSS model is designed to be a conclusive generalization of Pythagorean fuzzy sets, interval neutrosophic sets, and fuzzy soft sets. This combines the advantages of all the three previously established structures, as well as having user-customizable parameters and , thereby enabling the -INSS model to handle data of an unprecedentedly heterogeneous nature. The distance measure is a significant improvement over the current disputable distance measures, which handles the three types of membership values in a neutrosophic system as independent components, as if from a Euclidean vector. Lastly, the proposed algorithms were applied to data relevant to the ongoing COVID-19 pandemic which proves indispensable for the practical implementation of artificial intelligence.

[This retracts the article DOI: 10.1007/s00500-020-05387-5.].

[This retracts the article DOI: 10.1007/s00500-021-05909-9.].

Recently, image thresholding methods based on various entropy functions have been found popularity. Nonetheless, entropic-based methods depend on the spatial distribution of the grey level values in an image. Hence, the accuracy of these methods is limited due to the non-uniform distribution of the grey values. Further, the analysis of the COVID-19 X-ray images is evolved as an important area of research. Therefore, it is needed to develop an efficient method for the segmentation of the COVID-19 X-ray images. To address these issues, an efficient non-entropy-based thresholding method is suggested. A novel fitness function in terms of the segmentation score (SS) is introduced, which is used to reduce the segmentation error. A soft computing approach is suggested. An efficient optimizer using the chance-based birds' intelligence is introduced to maximize the fitness values. The new optimizer is validated utilizing the benchmark test functions. The statistical parameters reveal that the suggested optimizer is efficient. It shows a quite significant improvement over its counterparts-optimization based on seagull/cuckoo birds. Precisely, the paper includes three novel contributions-(i) fitness function, (ii) chance-based birds' intelligence for optimization, (iii) multiclass segmentation. The COVID-19 X-ray images are taken from the Kaggle Radiography database, to the experiment. Its results are compared with three different state-of-the-art entropy-based techniques-Tsallis, Kapur's, and Masi. For providing a statistical analysis, Friedman's mean rank test is conducted and our method Ranked one. Its superiority is claimed in terms of Peak Signal to Noise Ratio (PSNR), Feature Similarity Index (FSIM) and Structure Similarity Index (SSIM). On the whole, an improvement of about 11% in PSNR values is achieved using the proposed method. This method would be helpful for medical image analysis.

The score profiles could be used to measure learners' skills proficiency via cognitive diagnosis models (CDMs) for predicting their performance in the future examination. The prediction results could provide important decision-making supports for personalized e-learning instruction. However, facing the possible complexity of skills, the uncertainty of learners' skill proficiency and the large-scale volume of score profiles, the existing CDMs have limitations in the measurement mechanisms and diagnostic efficiency. In this paper, we proposed an approach based on a fuzzy cloud cognitive diagnosis framework (FC-CDF) to predicting examinees' performance in e-learning environment. In this approach, the normal cloud models (NCMs) are utilized innovatively to measure the expectation, degree of variation and variation frequency of learners' skill proficiency, and each NCM is transformed into an interval fuzzy number to characterize the uncertainty of the skill proficiency for every learner. Combining the educational psychology hypothesis with the parameter estimation method, we could obtain the learners' skill proficiency level and the slip and guess factors relevant to each test item, based on which the learners' scores could be predicted in a future test. Finally, the experiments demonstrate that the proposed approach provides good accuracy and significantly reduces execution time for predicting examinee performance, compared with the existing methods.

The rapid development of information technology has made a wide range of cutting-edge technologies accessible, supporting the flourishing of human existence. Modern technology has made it possible for new computer-based technological strategies like gamification. The pedagogical framework is based on the "gamification" game format, which is one of the most recent teaching strategies and has an engaging component for students. Gamification, flipped learning, and problem-based learning are three examples of the technical aspect of escape rooms. In the academic setting, gamification aims to boost student engagement and motivation in order to produce a better user experience. Gamification has been found to increase levels of participation, foster it, and improve activity outcomes. Gamification is recommended in educational settings to improve students' achievement, focus, and contentment in light of these benefits. In order to establish an effective learning environment where students may effectively improve their learning capacities and boost their performance, it can be difficult to select a higher performing technique among the available techniques due to the ongoing use of gamification techniques. The fuzzy analytical hierarchy process (FAHP) and evaluation based on distance from average solution (EDAS) are applied in order to determine the criterion weighting and assess the techniques in order to make a good decision. The presented paper analyzed numerous game-based learning techniques along with their applications in the educational field. Additionally, ten criteria and eight gamification methodologies are used to assess and pick the prior pertinent works. By utilizing the suggested approaches, the decision problem has been resolved. The FAHP approach is used in the suggested analysis to evaluate the criteria and determine their weights. Then, using the EDAS method, places are assigned to the chosen procedures based on their evaluation score and criterion weighting. The results of the appraisal show that the gamification technique with the highest production takes first place and is regarded as the best-performing and most successful technique. On the other hand, it is clear that the technique with the lowest production takes the bottom spot and is referred to as the least expensive and lowest performing technique. In order to increase students' motivation, which could have a substantial impact on learning, it has been discovered that gamification is a feasible strategy.

In this work, we intend to propose multiple hybrid algorithms with the idea of giving a choice to the particles of a swarm to update their position for the next generation. To implement this concept, Cuckoo Search Algorithm (CSA), Grey Wolf Optimization (GWO), Harris Hawks Optimization (HHO), and Whale Optimization Algorithm (WOA) have been utilized. Exhaustive possible combinations of these algorithms are developed and benchmarked against the base algorithms. These hybrid algorithms have been validated on twenty-four well-known unimodal and multimodal benchmarks functions, and detailed analysis with varying dimensions and population size is discussed for the same. Further, the efficacy of these algorithms has been tested on short-term electricity load and price forecasting applications. For this purpose, the algorithms have been combined with Artificial Neural Networks (ANNs) to evaluate their performance on the ISO New Pool England dataset. The results demonstrate that hybrid optimization algorithms perform superior to their base algorithms in most test cases. Furthermore, the results show that the performance of CSA-GWO is significantly better than other algorithms.