Protection of sensitive information has been always the major security concern since decades to withstand against illegitimate access and usage. Substitution-boxes (S-boxes) are vital components of any modern day cryptographic system that allows us to ensure its resistance to attacks. The prime problem with creating S-box is that we are generally unable to discover a consistent distribution among its numerous features to withstand diverse cryptanalysis attacks. The majority of S-boxes investigated in the literature has good cryptographic defenses against some attacks but are susceptible to others. Keeping these considerations in mind, this paper proposes a novel approach for S-box design based on a pair of coset graphs and a newly defined operation of row and column vectors on a square matrix. Several standard performance assessment criteria are used to evaluate the reliability of proposed approach, and the results demonstrate that the developed S-box satisfies all criterions for being robust for secure communication and encryption.

The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry that exists within different sources of information. In order to address this challenge, the primary aim of this study is to introduce novel Dombi operation concepts that are formulated within the framework of interval-valued Pythagorean fuzzy aggregation operators. In this study, an updated score function is presented to resolve the deficiency of the current score function in an interval-valued Pythagorean fuzzy environment. The concept of Dombi operations is used to introduce some interval-valued Pythagorean fuzzy aggregation operators, including the interval-valued Pythagorean fuzzy Dombi weighted arithmetic (IVPFDWA) operator, the interval-valued Pythagorean fuzzy Dombi ordered weighted arithmetic (IVPFDOWA) operator, the interval-valued Pythagorean fuzzy Dombi weighted geometric (IVPFDWG) operator, and the interval-valued Pythagorean fuzzy Dombi ordered weighted geometric (IVPFDOWG) operator. Moreover, the study investigates many important properties of these operators that provide new semantic meaning to the evaluation. In addition, the suggested score function and newly derived interval-valued Pythagorean fuzzy Dombi aggregation (IVPFDA) operators are successfully employed to select a subject expert in a certain institution. The proposed approach is demonstrated to be successful through empirical validation. Lastly, a comparative study is conducted to demonstrate the validity and applicability of the suggested approaches in comparison with current techniques. This research contributes to the ongoing efforts to advance the field of evaluation and decision-making by providing novel and effective tools and techniques.

Modern block ciphers deal with the development of security mechanisms to meet the security needs in several fields of application. The substitution box, which is an important constituent in block ciphers, necessarily has sufficient cryptographic robustness to counter different attacks. The basic problem with S-box design is that there is no evident pattern in its cryptographic properties. This study introduces a new mathematical algorithm for developing S-box based on the modular group coset graphs and a newly invented mathematical notion "matrix transformer". The proficiency of the proposed S-box is assessed through modern performance evaluation tools, and it has been observed that the constructed S-box has almost optimal features, indicating the effectiveness of the invented technique.

The primary objective of the water purification process is to remove harmful chemical compounds and microorganisms from water sources in order to produce water suitable for human consumption. Water purification satisfies the demand for drinkable water, which is a requirement for many industries, including the medical, pharmaceutical, and chemical industries, among others. Access to purified water is the single most important factor determining a nation’s strength and prosperity. As a consequence, researchers all over the world are investigating a wide variety of potential strategies for improving and preserving the water supply. In this paper, we present the findings of our research into a possible water strategy for purifying water and improving accessibility to drinkable water in areas prone to drought. This article presents the concepts of the complex intuitionistic fuzzy Dombi weighted averaging (CIFDWA) operator, the complex intuitionistic fuzzy Dombi ordered weighted averaging (CIFDOWA) operator, the complex intuitionistic fuzzy Dombi weighted geometric (CIFDWG) operator, and the complex intuitionistic fuzzy Dombi ordered weighted geometric (CIFDOWG) operator in complex intuitionistic fuzzy (CIF) settings. In addition, we investigate several important key features of these operators. Moreover, we introduce an improved score function to overcome the deficiencies of the existing score function under CIF knowledge. Furthermore, we effectively apply the proposed score function and newly defined operators to select the best technique for purifying water at a commercial scale. Additionally, we establish a comparative analysis to show the validity and feasibility of the proposed techniques compared to existing methods.

This paper explains the idea of t-intuitionistic fuzzy graphs as a powerful way to analyze and display relationships that are difficult to understand. The article also illustrates the ability of t-intuitionistic fuzzy graphs to establish complex relationships with multiple factors or dimensions of a physical situation under consideration. Moreover, the fundamental set operations of t-intuitionistic fuzzy graphs are proposed. The notions of homomorphism and isomorphism of t-intuitionistic fuzzy graphs are also introduced. Furthermore, the paper highlights a practical application of the proposed technique in the context of poverty reduction within a specific society. By employing t-intuitionistic fuzzy graphs, the research demonstrates the potential to address the multifaceted nature of poverty, considering various contributing factors and their interdependencies. This application showcases the versatility and effectiveness of t-intuitionistic fuzzy graphs as a tool for decision-making and policy planning in complex societal issues.

Every year, various experiments emerge in which a strong link between topological chemical structures and their properties is found. These properties are numerous such as melting point, boiling point, and drug toxicity. Topological index is the functional tool to determine these properties. This research paper will analyze some of the molecular drug structures, i.e., hyaluronic acid‐paclitaxel conjugates G_n, anticancer drug SP[n], polyomino chain of n‐cycle Z_n, triangular benzenoid T_n, and circumcoronene benzenoid series H_k using multicriteria decision‐making techniques including TOPSIS and SAW. The topological indices used in this research paper include the Randić index for α = 1, −1, 1/2, the augmented Zagreb index and the forgotten topological index.