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.

Amidst a transformative economic milieu in China, domestic enterprises are venturing into the global market, exposing them to intensified perils in international trade and investment. This research elucidates the international trade and investment (ITI) context within China, establishing criteria for ITI risk evaluation through an analytical exploration of international trade interactions. A methodology has been developed to quantify ITI risk, employing deep neural networks (DNNs), with a particular focus on the potential impact of edge cloud computing on China's trading economy. Through the utilization of convolutional neural networks (CNN), risks in China's trade and investment are appraised across various dimensions, exhibiting a noteworthy accuracy rate of 90.38%. It is identified that while CNN exhibits exemplary performance in estimating severe and high-risk scenarios, its efficacy diminishes when discerning general investment perils. The analysis underscores that a substantial portion of investments, constituting 14.8%, emanates from The Association of Southeast Asian Nations (ASEAN) and China, with market dynamics and macroeconomic conditions markedly influencing the risk associated with Chinese investments. By extending the utilization of deep learning (DL) in financial investments and integrating edge cloud computing, this investigation augments the capabilities for assessing China's ITI risk, providing a valuable resource for comprehending the ITI landscape within China.

Neutrosophic HyperSoft Set (NHSS) is a new approach towards computational intelligence and decision making under uncertainty. In this paper, we first consider distances for NHSS, and then propose similarity measures for NHSS. We also consider aggregated operation for aggregating NHSS decision matrix. TOPSIS (Technique for the order preference by similarity to ideal solution) is a strong approach for multi-criteria decision making (MCDM) which has been studied under various extensions of fuzzy sets. These approaches have drawbacks in depicting fuzzy decision-making information for handling MCDM situations under NHSS environment. To efficiently and accurately express fuzzy attribute values provided by decision-makers (DMs), we construct the TOPSIS based on the proposed distances and similarity measures of NHSS, called NHSS-TOPSIS. The proposed NHSS-TOPSIS provides the weights of DMs by utilizing similarity measures dependent on Hamming distance. We then aggregate the opinions of decision-makers using the proposed aggregated operation. Utilizing the relative closeness coefficient, we select the most ideal alternative in the proposed NHSS-TOPSIS procedures. To exhibit the relevance and adequacy of the proposed NHSS-TOPSIS, we apply it in a medical diagnosis and an optimal selection for the sustainable green security system. The proposed method reveals that the hypersoft set with the neutrosophic set theory can be very helpful to construct a connection between alternatives and attributes. It demonstrates that the proposed method is effective and useful in real applications.

Cosine and cotangent similarity measurements are critical in applications for determining degrees of difference and similarity between objects. In the literature, numerous similarity measures for various extensions of fuzzy set, soft set, Intuitionistic Fuzzy Sets (IFSs), Pythagorean Fuzzy Sets (PFSs) and HyperSoft Sets (HSSs) have been explored. Neutrosophic HyperSoft Sets (NHSSs), on the other hand, has fewer cosine and cotangent similarity measures. In this paper, we propose the trigonometric similarity measures of NHSSs. We further investigate the basic operators, theorems, and propositions for the proposed similarity measures. We know that global warming causes environmental problems. One of applications for solving global warming is the concept of renewable energy. To show the effectiveness of the proposed similarity measures, we apply them to renewable energy source selection problems. The study reveals the best geographical area to install the energy production units, under some technical attributive factors. To check the validity and superiority of the proposed work, it is compared with some existing techniques which reveal that, decision-making problems with further bifurcated attributes, have more accurate and precise results and can only be solved with this technique. In the future, the proposed techniques can be applied to case studies, in which attributes are more than one and further bifurcated along with more than one decision-maker. Also, this proposed work can be extended for several existing hybrids of hypersoft sets, intuitionistic hypersoft, neutrosophic hypersoft set, bi-polar hypersoft, m-polar hypersoft sets, and Pythagorean hypersoft set to solve Multi-Criteria Decision Making (MCDM) problems.

In decision-making scenarios, challenges often arise from closely knitted criteria or inherent uncertainties. Such uncertainties prominently pervade the realm of sustainable energy, particularly concerning hydrogen generation systems. A critical need is identified to elucidate the efficiency, costs, and environmental implications of these technologies as a shift towards a low-carbon economy is pursued. In this study, the interdependencies among decision-making variables were examined, revealing their collective influence and correlations. By utilizing the framework of Intuitionistic Hypersoft Sets (IHSSs), uncertainties were addressed, multi-criteria decision-making (MCDM) was harnessed, technological selection was facilitated, resource allocation was optimized, and environmental ramifications were assessed. The primary objective of this research was to decipher the conundrum of choosing among multiple hydrogen production methodologies. Such an approach fosters the adoption of environmentally conducive hydrogen production methods, heralding a shift towards a greener energy future. Notably, further research could probe into methodologies like AHP and TOPSIS in a neutrosophic context, offering tantalizing avenues for exploration.

This research paper presents a case study of a food chain in Pakistan that aims to transport its bakery products from the manufacturing unit in Islamabad to remote northern regions of the country while minimizing the total cost of distribution and transportation. The study employs various analytical methods, including linear programming, network optimization, and simulation modelling, to identify the optimal transportation solution that considers geographical barriers, infrastructural limitations, seasonal fluctuations, and regulatory constraints. The research delves into the underlying factors that contribute to the complexity and challenges of delivering goods to remote areas and explores the potential benefits of adopting a more holistic and integrated approach to transportation management. The study provides valuable insights and actionable recommendations for the Pakistani food chain and contributes to the broader field of transportation and logistics management.