Tessellations of kekulenes and cycloarenes have a lot of potential as nanomolecular belts for trapping and transporting heavy metal ions and chloride ions because they have the best electronic properties and pore sizes. The aromaticity, superaromaticity, chirality, and novel electrical and magnetic properties of a class of cycloarenes known as kekulenes have been the subject of several experimental and theoretical studies. Through topological computations of superaromatic structures with pores, we investigate the entropies and topological characterization of different tessellations of kekulenes. Using topological indices, the biological activity of the underlying structure is linked to its physical properties in (QSPR/QSAR) research. There is a wide range of topological indices accessible, including degree‐based indices, which are used in this work. With the total π‐electron energy, these indices have a lot of iteration. In addition, we use graph entropies to determine the structural information of a non‐Kekulean benzenoid graph. In this article, we study the crystal structure of non‐Kekulean benzenoid graph and then calculate some entropies by using the degree‐based topological indices. We also investigate the relationship between degree‐based topological indices and degree‐based entropies. This relationship is very helpful for chemist to study the physicochemical characterization of non‐Kekulean benzenoid chemical. These numerical values correlate with structural facts and chemical reactivity, biological activities, and physical properties.

Healthcare workers, including doctors and medical staff, must consistently make informed decisions that significantly affect patients on individual, community, national, and global scales. Healthcare practitioners must occasionally make judgments with constrained information, resources, and knowledge, yet it is anticipated that these choices are meticulously measured and precise. Familiarizing oneself with precise concepts pertaining to medical decision-making is essential. The complexity of decision-making (DM) arises from the environment’s ambiguous, imprecise, and uncertain characteristics, especially when several attributes are present and further categorized. We have used the hypersoft set concept to address such complex challenges. This article defines interval-valued Fermatean neutrosophic super hyper-soft sets. Its fundamental operations are subsets, equality, null sets, complements, unions, and intersections. Using these algebraic procedures, we establish a numerical example for the prioritization of patients awaiting organ transplantation. This hybrid environment may effectively manage uncertainty and yield distinctive results.

In this research, we first offer unique notions of averaging and geometric aggregation operators with confidence level by employing a probabilistic neutrosophic hesitant fuzzy rough framework. Then, we look into other descriptions of the suggested operators, such as idempotency, boundedness, and monotonicity. Additionally, for the derived operators, we establish the score and accuracy functions. We also provide a novel approach to assessing the selection procedure for smart medical devices (SMDs). The selection criteria for SMDs are quite complex, which is the most noteworthy feature of this investigation. It is suggested that these processes be simulated using a method utilizing a hesitant fuzzy set, a rough set, and a probabilistic single-valued neutrosophics set. The proposed approach is employed in the decision-making process, while taking into consideration the decision-makers’ (DMs’) level of confidence in the data they have obtained in order to deal with ambiguity, incomplete data, and uncertainty in lower and upper approximations. The major goal was to outline the issue’s complexities in order to pique interest among experts in the health care sector and encourage them to evaluate SMDs using various evaluation standards. The analysis of the technique’s outcomes demonstrated that the rankings and the results themselves were adequate and trustworthy. The effectiveness of our suggested improvements is also demonstrated through a symmetrical analysis. The symmetry behavior shows that the current techniques address more complex and advanced data.

Phenol formaldehyde (phenolic resin) has a wide range of moldings. However, it has immense consumption in manufacturing electrical equipment due to its insulating property. Phenolic resin retains properties at the freezing point, and also its age cannot be determined. Due to its insulator property, it has wide use in electrical equipment. In this article, degree-based topological indices of phenol formaldehyde are determined with the help of M-polynomial. We calculate the Zagreb index, Randić index, K-Banhatti indices, modified K-Banhatti indices, atom-bond connectivity index, geometric arithmetic index, symmetric index, inverse sum index, and harmonic index.

Monkeypox has recently re‐emerged. Since monkeypox has started to be seen in many countries without an epidemic, studies have started on new drugs used to treat this disease. Drug discovery is a challenging process. To alleviate this process, molecular descriptors used to predict the physical, chemical, and biological properties of chemical structures are studied. Molecular descriptors are numerical values of a chemical structure represented by a graph. In this study, M‐polynomial and neighborhood M‐polynomial molecular descriptors of drugs used and candidates for use in monkeypox are calculated and these descriptors are compared.

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the “optimal” solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads.