In this paper, we initiate the novel concept of complex intuitionistic fuzzy subgroups and prove that every complex intuitionistic fuzzy subgroup generates two intuitionistic fuzzy subgroups. We extend this ideology to define the concept of level subsets of complex intuitionistic fuzzy set and discuss its various fundamental algebraic characteristics. We also show that the level subset of the complex intuitionistic fuzzy subgroups is a subgroup. Furthermore, we investigate the homomorphic image and pre image of complex intuitionistic fuzzy subgroup under group homomorphism. Moreover, we prove that the product of two complex intuitionistic fuzzy subgroups is also a complex intuitionistic fuzzy subgroup and develop some new results about direct product of complex intuitionistic fuzzy subgroups.

In this paper, we introduce the idea of \(Q\)-complex fuzzy sub-ring (\(Q\)-CFSR) and discuss its various algebraic aspects. We prove that every \(Q\)-CFSR generates two \(Q\)-fuzzy sub-rings (\(Q\)-FSRs). We also present the concept of level subsets of \(Q\)-CFSR and show that level subset of \(Q\)-CFSR form sub-ring. Furthermore, we extend this idea to define the notion of the direct product of two \(Q\)-CFSR Moreover, we investigate the homomorphic image and inverse image of \(Q\)-CFSR.

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.

In quantitative structure-property and structure-activity relationships studies, several graph invariants, namely, topological indices have been defined and studied due to their numerous applications in computer networks, biotechnology, and nanochemistry. Topological indices are numeric parameters that describe the biological, physical, and chemical properties depending on the structure and topology of different chemical compounds. In this article, we inaugurated some degree-based novel indices, namely, geometric-harmonic , harmonic-geometric , neighborhood harmonic-geometric , and neighborhood geometric-harmonic indices and verified their chemical applicability. Furthermore, an attempt is made to calculate analytical closed formulas for different variants of silicon carbides and analyze the obtained results graphically.

Cardiovascular disease (CVD) is a leading global health concern. There is a critical need for accurate and reliable decision-making tools to select the optimal approach for diagnosing cardiovascular disease (CVD). In this study, we have addressed this pressing issue. Complex intuitionistic fuzzy set (CIFS) theory is adept at encapsulating vagueness due to its capability to encompass comprehensive problem specifications characterized by both intuitionistic uncertainty and periodicity. Within the scope of this article, we present two novel aggregation operators: the complex intuitionistic fuzzy dynamic weighted averaging (CIFDWA) operator and the complex intuitionistic fuzzy dynamic weighted geometric (CIFDWG) operator. Some intriguing characteristics of these operators are elucidated, and important special cases are also defined in detail. We devise an enhanced score function to rectify the deficiencies observed in the existing score function under complex intuitionistic fuzzy knowledge. Furthermore, these operators are employed in the development of a systematic approach for the handling of multiple attribute decision-making (MADM) scenarios involving complex intuitionistic fuzzy data. Moreover, we undertake the resolution of an MADM problem, wherein we ascertain the optimal approach for diagnosing cardiovascular disease (CVD) through the utilization of the proposed operators, thereby substantiating their utility in decision-making processes. Finally, we conduct a comprehensive comparative analysis, pitting the presented operators against an array of existing counterparts, in order to demonstrate the reliability and stability inherent in the derived methodologies.