The success of AES encryption standard created challenges for the cryptographers to construct strong substitution-boxes using different underlying approaches. It is because they are solely responsible to decide the robustness of cryptosystem against linear and differential cryptanalyses. With an aim to fulfill the mentioned requirement of robustness, a novel group theoretic and graphical method is proposed to construct S-box with optimal features. Firstly, a strong S-box is generated with the help of orbits of coset graphs and the action of proposed powerful permutation of symmetric group S256. In addition, a specific group is designed the action of whose pairs of permutations has the ability to generate as many as 462422016 strong S-boxes. Few of such proposed S-boxes are reported and assessed against standard performance parameters to validate the effectiveness of proposed findings. The features of proposed S-boxes are compared with most of the recent S-boxes to validate the superior performance. Moreover, they are also applied for image encryption to demonstrate their suitability for multimedia security applications.

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.

The concept of interval-valued intuitionistic fuzzy sets (IVIFSs) presents a compelling and practical framework for modeling real-world problems. In various fields, such as pattern recognition and decision-making, the development of similarity measures tailored to this class holds significant importance. These measures play a pivotal role in the decision-making process involving IVIFSs, as they quantify the extent of similarity between two such sets. In this article, the shortcomings of the existing similarity measures within the framework of IVIFSs are highlighted, and an improved similarity measure is presented. A comparative study validates that this new similarity measure is better than the existing measures in the IVIF environment. This study systematically establishes several essential properties of the novel similarity measure and substantiates its effectiveness through numerical illustrations. Moreover, a comparative assessment is undertaken to validate the efficacy of the recently introduced measure in relation to established metrics, within the context of IVIFSs. To address the evaluation of software quality, a dedicated mechanism is devised, harnessing the proposed IVIFS similarity measure. Furthermore, an innovative production strategy is formulated utilizing the newly defined methodology to determine the optimal approach for the production of a specific product.

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.

In this study, we propose the concept of t-intuitionistic fuzzy order of an element of a t-intuitionistic fuzzy subgroup (t-IFSG) of a finite group and examine different important algebraic properties of this phenomena. We also prove many useful algebraic aspects of this notion for a cyclic group. Moreover, we extend this ideology to define t-intuitionistic fuzzy order and index of a t-IFSG of group. In addition, we establish t-intuitionistic fuzzification of Langrange’s theorem.