The correlation coefficient between two variables is an important aspect of statistics. The accuracy of assessments of correlation relies on information from a set of discourses. Data collected in statistical studies are often full of exceptions. Pythagorean fuzzy soft sets (PFSS) are a parametrized family of extended Pythagorean fuzzy sets (PFS). They comprise a generalization of intuitionistic fuzzy soft sets which may be used to accurately assess deficiencies and uncertainties in evaluations. PFSS can accommodate uncertainty more competently than intuitionistic fuzzy soft sets and are the most important strategy when dealing with fuzzy information in decision-making processes. Herein, the concept and characteristics of correlation coefficients and the weighted correlation coefficients in PFSS are discussed. We also introduce the Pythagorean fuzzy soft weighted average (PFSWA) and Pythagorean fuzzy soft weighted geometric (PFSWG) operators and discuss their desirable characteristics. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under the PFSS environment based on correlation coefficients and weighted correlation coefficients will be introduced. Through the proposed methodology, a technique for decision-making is developed. Additionally, an application of the proposed TOPSIS technique is presented for green supplier selection in green supply chain management (GSCM). The practicality, efficacy, and flexibility of the proposed approach is proved through comparative analyses, drawing upon existing studies.

The electrocardiogram (ECG) is one of the most widely used diagnostic instruments in medicine and healthcare. Deep learning methods have shown promise in healthcare prediction challenges involving ECG data. This paper aims to apply deep learning techniques on the publicly available dataset to classify arrhythmia. We have used two kinds of the dataset in our research paper. One dataset is the MIT‐BIH arrhythmia database, with a sampling frequency of 125 Hz with 1,09,446 ECG beats. The classes included in this first dataset are N, S, V, F, and Q. The second database is PTB Diagnostic ECG Database. The second database has two classes. The techniques used in these two datasets are the CNN model, CNN + LSTM, and CNN + LSTM + Attention Model. 80% of the data is used for the training, and the remaining 20% is used for testing. The result achieved by using these three techniques shows the accuracy of 99.12% for the CNN model, 99.3% for CNN + LSTM, and 99.29% for CNN + LSTM + Attention Model.

This study presents a novel deep learning-based superresolution framework for enhancing remote sensing imagery to assess groundwater quality and environmental conditions in Lahore, Pakistan. We developed a convolutional neural network architecture that upscales low-resolution satellite imagery to generate high-resolution (0.5m) outputs, achieving a peak signal-to-noise ratio (PSNR) of 32.4 dB and structural similarity index (SSIM) of 0.91. The enhanced imagery enabled precise delineation of urban features and environmental parameters affecting groundwater quality. Using the super-resolved images alongside traditional water quality parameters (pH, hardness, TDS) analyzed through Fuzzy AHP, we calculated the Groundwater Quality Index (GWQI) for 33 areas across four years (2008-2020). Results showed most areas achieved “Better water” quality status by 2020, though two regions (Old City and Anarkali) were classified as “Poor water” quality. We observed a moderate negative correlation (r = -0.62, p < 0.001) between GWQI and static water level depth, with significant depth increases in areas like Dholanwal (37.1m), Ichhra (47.06m), and Township (49.35m) by 2020. The integration of super-resolution remote sensing with conventional water quality assessment demonstrates promising applications for urban environmental monitoring and groundwater resource management.

The correlation coefficient between the two parameters plays a significant part in statistics. Furthermore, the exactness of the assessment of correlation depends upon information from the set of discourses. The data collected for various statistical studies are full of ambiguities. The idea of interval-valued intuitionistic fuzzy soft sets is an extension of intuitionistic fuzzy soft sets that is used to express insufficient evaluation, uncertainty, and anxiety in decision-making. Intuitionistic fuzzy soft sets consider two different types of information, such as membership degree and nonmembership degree. In this paper, the concepts and properties of the correlation coefficient and the weighted correlation coefficient of interval-valued intuitionistic fuzzy soft sets are proposed. A prioritization technique for order preference by similarity to the ideal solution based on interval-valued intuitionistic fuzzy soft sets of correlation coefficients and the weighted correlation coefficient is introduced. We also proposed interval-valued intuitionistic fuzzy soft weighted average and interval-valued intuitionistic fuzzy soft weighted geometric operators and developed decision-making techniques based on the proposed operators. By using the developed techniques, a method for solving decision-making problems is proposed. To ensure the applicability of the proposed methods, an illustrative example is given. Finally, we present a comparison of some existing methods with our proposed techniques.

In this paper, we investigate the multi-criteria decision-making complications under intuitionistic fuzzy hypersoft set (IFHSS) information. The IFHSS is a proper extension of the intuitionistic fuzzy soft set (IFSS) which discusses the parametrization of multi-sub attributes of considered parameters, and accommodates more hesitation comparative to IFSS utilizing the multi sub-attributes of the considered parameters. The main objective of this research is to introduce operational laws for intuitionistic fuzzy hypersoft numbers (IFHSNs). Additionally, based on developed operational laws two aggregation operators (AOs), i.e., intuitionistic fuzzy hypersoft weighted average (IFHSWA) and intuitionistic fuzzy hypersoft weighted geometric (IFHSWG), operators have been presented with their fundamental properties. Furthermore, a decision-making approach has been established utilizing our developed aggregation operators (AOs). Through the established approach, a technique for solving decision-making (DM) complications is proposed to select sustainable suppliers in sustainable supply chain management (SSCM). Moreover, a numerical description is presented to ensure the validity and usability of the proposed technique in the DM process. The practicality, effectivity, and flexibility of the current approach are demonstrated through comparative analysis with the assistance of some prevailing studies.

The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set (PFHSS) is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set (IFHSS), which is used to accurately assess insufficiency, anxiety, and uncertainties in decision‐making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision‐making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators such as Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators under the PFHSS scenario. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under PFHSS based on correlation coefficients and weighted correlation coefficients is presented. Through the developed methodology, a technique for solving multiattribute group decision‐making (MAGDM) problem is planned. Also, the importance of the developed methodology and its application in indicating multipurpose antivirus mask throughout the COVID‐19 pandemic period is presented. A brief comparative analysis is described with the advantages, effectiveness, and flexibility of numerous existing studies that demonstrate the effectiveness of the proposed method.