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The fundamental goal of this study was to achieve the Ricci curvature inequalities for a skew CR-warped product (SCR W-P) submanifold isometrically immersed in a complex space form (CSF) in the expressions of the squared norm of mean curvature vector and warping functions (W-F). The equality cases were likewise examined. In particular, we also derived Ricci curvature inequalities for CR-warped product (CR W-P) submanifolds. To sustain this study, an example of these submanifolds is provided.

This study explores the coherent control of the photonic spin hall shift through a configuration involving a four-levels dielectric medium. The probe beam engages with a cavity containing a four-level dielectric medium. By adjusting the parameters of the driving fields, the photonic spin shift can be controlled to exhibit either positive or negative values. The maximum values of the spin hall shift is in the range of with the incidence angle ( = 1.2 radian and 3 radian ) and the minimum values is reported as against the probe field detuning ( and ). The results hold significant potential for use in fields like sensing devices, spin-based electronics, magnetic storage and quantum information processing.

Metal–organic frameworks (MOFs) are vital in modern material science, offering unique properties for gas storage, catalysis, and drug delivery due to their highly porous and customizable structures. Chemical graph theory emerges as a critical tool, providing a mathematical model to represent the molecular structure of these frameworks. Topological indices/molecular descriptors are mathematical formulations applied to molecular models, enabling the analysis of physicochemical properties and circumventing costly lab experiments. These descriptors are crucial for quantitative structure-property and structure-activity relationship studies in mathematical chemistry. In this paper, we study the different molecular descriptors of tetracyanobenzene metal–organic framework. We also give numerical comparison of computed molecular descriptors.

In the context of telecommunications, AI enhances network efficiency by predicting and managing traffic. In many decision-making scenarios, decision-makers choose the more flexible structure that can handle all kinds of information. Bipolarity is the only case in which we can discuss the positive and negative aspects of certain scenarios. On one side, AI enhances network efficiency, proactive maintenance, and personalized customer experience but on the other hand, it has also some negative aspects (1) implementing AI infrastructure can be costly (2) Uses of AI in telecommunication may raise data security concerns and user privacy (3) AI can lead to potential issues if system fail or misused. To cover these issues, the idea of an interval-valued bipolar fuzzy soft set (IVBFSS) has been developed that can deal with both positive and negative aspects of AI. Some basic operational laws for IVBPFS numbers are developed. Several fundamental aggregation operators have been introduced like arithmetic average and geometric average aggregation operators, indicating our main contribution. An algorithm is developed to discuss the application perspective of the initiated approaches. We have utilized these developed notions to classify AI-driven techniques in the telecommunications sector to discuss the applicability of the initiated notions. A comparative analysis of the developed approaches shows the advantages and superiority of the introduced work.

Tracking the development of disability conditions presents significant challenges due to uncertainty, imprecision, and dynamic health progression patterns. Traditional multi-criteria decision-making (MCDM) techniques often struggle with such complex and fuzzy medical data. To address this gap, we propose a novel classification framework based on Tamir’s complex fuzzy Aczel-Alsina weighted aggregated sum product assessment (WASPAS) approach. This hybrid model incorporates complex fuzzy logic to handle multidimensional uncertainty and utilizes the Aczel-Alsina function for flexible aggregation. We apply this method to evaluate and classify AI-powered predictive models used for monitoring disability progression. The proposed framework not only improves classification accuracy but also enhances decision support in healthcare planning. A case study validates the robustness, sensitivity, and effectiveness of the proposed method in real-world disability tracking scenarios.

Fuzzy sets can model the inherent ambiguity and subjectivity in disability assessment by allowing for flexible classification and decision-making. This contributes to the development of flexible clinical support systems that are effective in meeting individual needs. Subjective assessments of an individual’s needs and talents are common in disability. Conventional clear-cut methodologies classify people as “disabled” or \"not disabled,\" which may not fully reflect the wide range of disabilities. Fuzzy sets allow for degrees of membership, such as (a) Person A has 70% mobility impairment. (b) Person B needs 50% personal care support. This method takes into account the subjectivity and variability of disability assessments. Designing adaptive systems for people with disabilities requires the use of fuzzy sets for clinical support. For this purpose, we have proposed the theory of aggregation operators based on a complex fuzzy set. Aggregation operators help us to convert overall information to a single value that can help our clinical support system. Moreover, for the application of the delivered approach, we have proposed an algorithm and utilized this approach for the selection of the best disability support system. We have provided a comparative analysis of the defined theory to discuss the advantages of the initiated work.

Mathematical tools are crucial for dealing with uncertainty because they provide a rigorous and logical framework for evaluating, measuring, and making decisions in the presence of ambiguous information. The bipolar complex fuzzy is one of the mathematical methods for simultaneously handling dual aspect and second-dimensional information. Thus, in this script, we propound aggregation operators “partitioned Maclaurin symmetric mean and partitioned dual Maclaurin symmetric mean” within bipolar complex fuzzy set that is bipolar complex fuzzy partitioned Maclaurin symmetric mean and bipolar complex fuzzy partitioned dual Maclaurin symmetric mean, bipolar complex fuzzy weighted partitioned Maclaurin symmetric mean and bipolar complex fuzzy weighted partitioned dual Maclaurin symmetric mean operators. We also propound the related axioms of the invented operators. By employing the deduced aggregation operators, we produce a technique of multiattribute decision making within bipolar complex fuzzy sets to overcome awkward uncertainties. After that, we demonstrate an explanatory example for revealing the significance and practicability of the deduced theory and then we analyze the reliability and legitimacy of the propounded operators by comparing them with some prevailing work.

This paper proposes an innovative image encryption scheme exploiting the chaotic nature of a four-dimensional chaotic system and the computational capability of Langton’s Ant cellular automaton. Traditional three-dimensional chaotic systems often have restricted key space and limited complexity, making them vulnerable to cryptanalysis. To address these limitations, the proposed scheme integrates multi-layered transformations, including chaotic diffusion, symbolic encoding, and dynamic keystream generation. Comprehensive security analyses demonstrate that the proposed scheme achieves near-optimal results, including a large key space of approximately 1 , high entropy (7.9977), and excellent differential attack resistance indicated by NPCR ( 99.61%) and UACI ( 33.44%) metrics. The proposed method effectively disrupts pixel correlations, providing robust protection against various cryptographic threats. These results confirm that our encryption approach offers a secure, efficient, and practical solution for protecting multimedia data in modern digital communication systems.

We explore the Geometrization of hyperbolic conformal Ricci solitons and examine the properties of bulk viscous fluid string spacetime in conjunction with the hyperbolic conformal Ricci solitons in this research note. A ∅ ( Q ) -vector field and a Ricci bi-conformal vector field that admits the hyperbolic conformal Ricci solitons were also used to interact with the bulk viscous fluid string spacetime. It is proven that the bulk viscous fluid string spacetime admits the hyperbolic conformal Ricci solitons with a proper ∅ ( Q ) -vector field, and the bulk viscous fluid string spacetime holds Ricci collineation, then the spacetime is an Einstein manifold, and hyperbolic conformal Ricci soliton is identified as a conformal Ricci soliton. Additionally, using a scalar concircular field, we study the gradient hyperbolic conformal Ricci solitons in bulk viscous fluid string spacetime and talk about the gradient hyperbolic conformal Ricci solitons’ rate of change. Finally, using a scalar concircular field and a gradient hyperbolic conformal Ricci solitons, we calculated the energy conditions for a bulk viscous fluid string spacetime.

The integration of AI simulation models within smart electrical prosthetic systems represents a significant advancement in disability disease diagnosis. However, the selection and evaluation of these AI models interpret some multi-criteria decision-making dilemmas because of the presence of uncertainty and bipolarity (positive and negative aspects) of the selection criteria. Current literature lacks the selection and evaluation of AI simulation models that consider both bipolarity and uncertainty of the criteria, while prevailing Choquet integral aggregation operators despite their strong capabilities for handling information relationships, fail to efficiently process bipolar fuzzy information. The existence of this limitation makes it challenging to identify element interactions and non-linear relationships in uncertain environments containing both positive and negative aspects. To overcome these gaps, first, we develop two operators that are the bipolar fuzzy Choquet integral averaging and bipolar fuzzy Choquet integral geometric operators that uniquely integrate dual aspects (bipolarity) with criterion interaction modeling capabilities, fundamentally differing from traditional fuzzy approaches that cannot simultaneously process dual aspects of criterion. Secondly, we design a new multi-criteria decision-making approach using these operators to assess AI simulation models for prosthetic systems, since the criteria involved such as diagnostic accuracy, computational efficiency, and system reliability, have both positive and negative aspects that need to be considered together. Our method was applied in detail to select AI simulation models for smart electrical prosthetic systems and compared with some prevailing methods and standard Choquet integral approaches. This showed that our method is more precise and produces better evaluation results. It introduces a new theoretical basis for bipolar fuzzy Choquet integral aggregation and offers medical professionals a reliable way to pick the best AI simulation models for important prosthetic applications that influence patient outcomes and the functioning of prosthetics.