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The prevalence of cardiovascular disease (CVD) is a major issue in world health. There is a compelling desire for precise and effective methods for making decisions to determine the most effective technique for treating CVD. Here, we focused on the urgent matter at hand. Pythagorean fuzzy dynamic settings are exceptionally proficient at capturing ambiguity because they can handle complex problem specifications that involve both Pythagorean uncertainty and periodicity. In this article, we introduced a pair of novel aggregation operators: The Pythagorean fuzzy dynamic ordered weighted averaging (PFDOWA) operator and the Pythagorean fuzzy dynamic ordered weighted geometric (PFDOWG) operator, and we proved various structural properties of these concepts. Using these operators, we devised a systematic methodology to handle multiple attribute decision-making (MADM) scenarios incorporating Pythagorean fuzzy data. Moreover, we endeavored to address a MADM problem, where we discerned the most efficacious strategy for the management of CVD through the application of the proposed operators. Finally, we undertook an exhaustive comparative analysis to evaluate the ability of the suggested methods in connection with several developed procedures, therefore demonstrating the reliability of the generated methodologies.

Abstract The resilient framework of Linguistic Intuitionistic Fuzzy Sets (LIFSs) allows for the representation and management of uncertainties related to intuitionistic judgments and linguistic expressions. Recent advances in passive and active safety systems have reduced highway fatalities. Autonomous vehicles can improve safety, efficiency, and mobility by navigating traffic without a driver. One of the primary benefits associated with this technology is that it reduces the number of traffic collisions that result in millions of fatalities and numerous injuries. In this research work, we devise two novel aggregation operators: the linguistic intuitionistic fuzzy Dombi ordered weighted averaging (LIFDOWA) operator and the linguistic intuitionistic fuzzy Dombi ordered weighted geometric (LIFDOWG) operator, and explore their fundamental structural properties. We provide innovative score and accuracy functions for multiple attribute decision-making (MADM) problems within the framework of LIF knowledge. Moreover, we use these techniques to develop a specialized algorithm for MADM issues that addresses the complexities arising from ambiguous data during the selection process. We also demonstrate the effectiveness of our proposed methods by applying them to solve the MADM scenario of selecting an optimal approach to improve the credibility of autonomous vehicle control systems on a commercial scale. In addition, we also compare and evaluate the authenticity and practicability of the newly designed techniques in comparison to existing methodologies.

Abstract The Web 3.0 network system, the next generation of the world wide web, incorporates new technologies and algorithms to enhance accessibility, decentralization, and security, mimicking human comprehension and enabling more personalized user interactions. The key component of this environment is decentralized identity management (DIM), embracing an identity and access management strategy that empowers computing devices and individuals to manage their digital personas. Aggregation operators (AOs) are valuable techniques that facilitate combining and summarizing a finite set of imprecise data. It is imperative to employ such operators to effectively address multicriteria decision-making (MCDM) issues. Yager operators have a significant extent of adaptability in managing operational environments and exhibit excellent effectiveness in addressing decision-making (DM) uncertainties. The complex spherical fuzzy (CSF) model is more effective in capturing and reflecting the known unpredictability in a DM application. This research endeavors to enhance the DM scenario of the Web 3.0 environment using Yager aggregation operators within the CSF environment. We present two innovative aggregation operators, namely complex spherical fuzzy Yager-ordered weighted averaging (CSFYOWA) and complex spherical fuzzy Yager-ordered weighted geometric (CSFYOWG) operators. We elucidate some structural characteristics of these operators and come up with an updated score function to rectify the drawbacks of the existing score function in the CSF framework. By utilizing newly proposed operators under CSF knowledge, we develop an algorithm for MCDM problems. In addition, we adeptly employ these strategies to handle the MCDM scenario, aiming to identify the optimal approach for ensuring the privacy of digital identity or data in the evolving landscape of the Web 3.0 era. Moreover, we undertake a comparative study to highlight the veracity and proficiency of the proposed techniques compared to the previously designed approaches.

Abstract Bioremediation techniques, which harness the metabolic activities of microorganisms, offer sustainable and environmentally friendly approaches to contaminated soil remediation. These methods involve the introduction of specialized microbial consortiums to facilitate the degradation of pollutants, contribute to soil restoration, and mitigate environmental hazards. When selecting the most effective bioremediation technique for soil decontamination, precise and dependable decision-making methods are critical. This research endeavors to tackle the aforementioned concern by utilizing the tool of aggregation operators in the framework of the Linguistic Intuitionistic Fuzzy (LIF) environment. Linguistic Intuitionistic Fuzzy Sets (LIFSs) provide a robust framework for representing and managing uncertainties associated with linguistic expressions and intuitionistic assessments. Aggregation operators enrich the decision-making process by efficiently handling the intrinsic uncertainties, preferences, and priorities of MADM problems; as a consequence, the decisions produced are more reliable and precise. In this research, we utilize this concept to devise innovative aggregation operators, namely the linguistic intuitionistic fuzzy Dombi weighted averaging operator (LIFDWA) and the linguistic intuitionistic fuzzy Dombi weighted geometric operator (LIFDWG). We also demonstrate the critical structural properties of these operators. Additionally, we formulate novel score and accuracy functions for multiple attribute decision-making (MADM) problems within LIF knowledge. Furthermore, we develop an algorithm to confront the complexities associated with ambiguous data in solving decision-making problems in the LIF Dombi aggregation environment. To underscore the efficacy and superiority of our proposed methodologies, we adeptly apply these techniques to address the MADM problem concerning the optimal selection of a bioremediation technique for soil decontamination. Moreover, we present a comparative evaluation to delineate the authenticity and practical applicability of the recently introduced approaches relative to previously formulated techniques.

There is increasing concern over the environmental risks associated with deepwater petroleum exploration activities. The integration of environmental risk assessment and oil spill modeling can help to understand and quantitatively characterize the potential risks from subsea blowouts in specific regions. This study integrates a novel deepwater oil spill model (DWOSM) and an extended stochastic modeling methodology to assess the environmental risk of polycyclic aromatic hydrocarbons (PAHs) during a simulated offshore subsurface blowout off the east coast of Newfoundland, Canada. Additionally, the effectiveness of subsea dispersant injection (SSDI) in spill mitigation was investigated through comparative simulations. Resultant spill hazard and risk maps for current and proposed areas of offshore oil and gas development, in support of contingency plans, revealed that surfaced oil tends to drift toward the southeast and east in the hypothetical blowout case; nearshore areas of east Newfoundland have relatively low risk shortly after a deep-sea blowout; released PAHs may elicit more adverse ecological impacts than volatile organic compounds (VOCs); and SSDI application can reduce contaminant exposure levels but at the expense of enlarging the impacted zone for a short term. This stochastic simulation-based risk assessment provides scientific evidence to support decision-making in strategic oil spill response operations.

Major depressive disorder (MDD) with suicidal ideation or behaviour (MDSI) is associated with an increased risk of future suicide. The timely identification of suicide risk in patients with MDD and the subsequent implementation of interventions are crucially important to reduce their suffering and save lives. However, the early diagnosis of MDSI remains challenging across the world, as no objective diagnostic method is currently available. In China, the challenge is greater due to the social stigma associated with mental health problems, leading many patients to avoid reporting their suicidal ideation. Additionally, the neural mechanisms underlying MDSI are still unclear, which may hamper the development of effective interventions. We thus conducted this narrative review to summarise the existing neuroimaging studies of MDSI in Chinese patients, including those involving structural magnetic resonance imaging (MRI), functional MRI, neuronal electrophysiological source imaging of the brain dynamics with electroencephalography and magnetoencephalography. By synthesising the current research efforts in neuroimaging studies of Chinese patients with MDSI, we identified potential objective neuroimaging biomarkers, which may aid in the early identification of patients with MDSI who are at high suicide-related risk. Our findings also offer insights into the complex neural mechanisms underlying MDSI and suggest promising therapeutic targets. Furthermore, we propose future directions to discover novel imaging signatures, improve patient care, as well as help psychiatrists and clinical investigators plan their future research.

Abstract The concept of interval-valued intuitionistic fuzzy sets is intellectually stimulating and holds significant utility in the representation and analysis of real-world problems. The development of similarity measures within the class of interval-valued intuitionistic fuzzy sets possesses significant importance across various academic disciplines, particularly in the fields of decision-making and pattern recognition. The utilization of similarity measures is of utmost importance in the decision-making process when implementing interval-valued intuitionistic fuzzy sets. This is due to its inherent capability to quantitatively assess the level of resemblance or similarity between two interval-valued intuitionistic fuzzy sets. In this article, the drawbacks of the existing similarity measures in the context of an interval-valued intuitionistic fuzzy environment are addressed, and a novel similarity measure is presented. Many fundamental properties of this new interval-valued intuitionistic fuzzy similarity measure are also established, and the effectiveness of this similarity measure is illustrated by presenting a useful example. Moreover, a comparison is given to demonstrate the validity of the newly proposed similarity measure within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment. In addition, an algorithm is designed to solve multi-criteria decision making problems by means of the proposed measure in the interval-valued intuitionistic fuzzy setting. Furthermore, this newly defined similarity measure is successfully applied to select an optimal renewable energy source to reduce energy crises. Finally, we conduct a comparative study to showcase the authenticity of the recently defined technique within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment.

Abstract This article comprises the study of class S E ∗ $\mathcal{S}_{E}^{\ast }$ that represents the class of normalized analytic functions f satisfying ς f ′ ( z ) / f ( ς ) ≺ sec h ( ς ) ${\varsigma \mathsf{f}}^{\prime }(z)/\mathsf{f}( {\varsigma })\prec \sec h ( \varsigma ) $ . The geometry of functions of class S E ∗ $\mathcal{S}_{E}^{\ast }$ is star-shaped, which is confined in the symmetric domain of a secant hyperbolic function. We find sharp coefficient results and sharp Hankel determinants of order two and three for functions in the class S E ∗ $\mathcal{S}_{E}^{\ast }$ . We also investigate the same sharp results for inverse coefficients.

The complex anti-fuzzy set (CAFS) is an extension of the traditional anti-fuzzy set with a wider range for membership function beyond real numbers to complex numbers with unit disc aims to address the uncertainty of data. The complex anti-fuzzy set is more significant because it provides two dimensional information and versatile representation of vagueness and ambiguity of data. In terms of the characteristics of complex anti-fuzzy sets, we proposed the concept of $ (\epsilon, \delta) $-CAFSs that offer a more comprehensive representation of the uncertainty of data than CAFSs by considering both the magnitude and phase of the membership functions and explain the $ \left(\epsilon, \delta \right) $-complex anti fuzzy subgroups (CAFS) in the context of CAFSs. Moreover, we showed that everyCAFSGis a $ (\epsilon, \delta) $-CAFSG. Also, we used this approach to define $ (\epsilon, \delta) $-complex anti-fuzzy(CAF) cosets and $ (\epsilon, \delta) $-CAF normal subgroups of a certain group as well as to investigate some of their algebraic properties. We elaborated the $ (\epsilon, \delta) $-CAFSG of the classical quotient group and demonstrated that the set of all $ (\epsilon, \delta) $-CAF cosets of such a particular CAFs normal subgroup formed a group. Furthermore, the index of $ \left(\epsilon, \delta \right) $-CAFSG was demonstrated and $ (\epsilon, \delta) $-complex anti fuzzification of Lagrange theorem corresponding to the Lagrange theorem of classical group theory was briefly examined.

The need to meet current energy demands while protecting the interests of future generations has driven people to adopt regulatory frameworks that promote the careful use of limited resources. Among these resources, the sun is an everlasting source of energy. Solar energy stands out as a prime example of a renewable and environmentally friendly energy source. An imperative requirement exists for precise and dependable decision-making methods for the selection of the most efficacious solar cell. We aimed to address this particular issue. The theory of complex intuitionistic fuzzy sets (CIFS) adeptly tackles ambiguity, encompassing complex problem formulations characterized by both intuitionistic uncertainty and periodicity. We introduced two aggregation operators: The complex intuitionistic fuzzy dynamic ordered weighted averaging (CIFDOWA) operator and the complex intuitionistic fuzzy dynamic ordered weighted geometric (CIFDOWG) operator. Noteworthy features of these operators were stated, and significant special cases were meticulously outlined. An updated score function was devised to address the deficiencies, identified in the current score function within the context of CIF knowledge. In addition, we devised a methodical strategy for managing multiple attribute decision-making (MADM) problems that involve CIF data by implementing the proposed operators. To demonstrate the efficacy of the formulated algorithm, we presented a numerical example involving the selection of solar cells together with a comparative analysis with several well-established methodologies.

Selecting the right Biometric-Based Attendance Device (BBAD) is pivotal for enhancing security, operations, and compliance in today’s dynamic environment of identity authentication.Addressing the complexities arising from uncertainty and periodicity, the Complex Fermatean Fuzzy Set (CFFS) theory emerges as adept, encapsulating comprehensive problem specifications. This study introduces two innovative aggregation operators within the CFFS framework: the Complex Fermatean Fuzzy Dynamic Weighted Averaging (CFFDWA) and the Complex Fermatean Fuzzy Dynamic Weighted Geometric (CFFDWG) operators. Some important characteristics of the newly defined operators are established. The shortcomings in the existing score function are rectified along with the introduction of a novel enhanced score function under complex Fermatean fuzzy environment. Moreover, these operators contribute to a systematic framework for handling Multiple Attribute Decision Making (MADM) problems involving complex Fermatean fuzzy information. The article exemplifies their application in resolving a MADM problem, determining the optimal model of BBAD. Finally, to validate the derived methodologies, a thorough comparison study is carried out, demonstrating the superiority of the presented operators against various existing operators.

The significance of t-intuitionistic fuzzy TOPSIS lies in its ability to address challenges related to uncertainty and ambiguity within the decision-making process. The incorporation of the “t” parameter as a t-norm and t-conorm operator offers a more comprehensive and precise approach, making it essential in scenarios where standard intuitionistic fuzzy TOPSIS approaches are insufficient. The implementation of this methodology across multiple domains enhances the dependability and robustness of decision-making procedures. The classification of the technique as an indispensable tool with a broad spectrum of applications is substantially bolstered by its fundamental qualities of versatility, adaptability, and flexibility. In this study, we introduce a novel distance measure called the lift-distance measure between t-intuitionistic fuzzy sets and examines its structural properties. Then, the superiority of this new distance measure is compared with some existing distance measures. To address circumstances with inherent ambiguity, we present a novel decision-making tool called the t-intuitionistic fuzzy TOPSIS technique based on the proposed distance measure. The integration of t-intuitionistic fuzzy terminology into this approach augments the versatility and inclusiveness of the TOPSIS methodology. The case analysis demonstrates that the developed strategy’s effectiveness and precision are superior to those of established alternatives. By providing a flexible and all-encompassing tool for decision-making in conditional environments, the application of this methodology possesses the capacity to generate significant favorable results. In addition, a comparative analysis is undertaken, which includes established TOPSIS methods, to demonstrate the improved performance of the proposed method. The comparison results demonstrate the ability of the proposed method to effectively capture the imprecision or vague differences in t-intuitionistic fuzzy sets so as to obtain more accurate and reliable ranking results.

Abstract Two new subclasses of the class of bi-Bazilevič functions, which are related to the Fibonacci-number series and the square-root functions, are introduced and studied in this article. Under a special choice of the parameter involved, these two classes of Bazilevič functions reduce to two new subclasses of star-like biunivalent functions related with the Fibonacci-number series and the square-root functions. Using the Faber polynomial expansion (FPE) technique, we find the general coefficient bounds for the functions belonging to each of these classes. We also find bounds for the initial coefficients for bi-Bazilevič functions and demonstrate how unexpectedly these initial coefficients behave in relation to the square-root functions and the Fibonacci-number series.

Emerging technology selection is crucial for enterprise integration, driving innovation, competitiveness, and streamlining operations across diverse sectors like finance and healthcare. However, the decision-making process for technology adoption is often complex and fraught with uncertainties. Bipolar fuzzy sets offer a nuanced representation of uncertainty, allowing for simultaneous positive and negative membership degrees, making them valuable in decision-making and expert systems. In this paper, we introduce dynamic averaging and dynamic geometric operators under bipolar fuzzy environment. We also establish some of the fundamental crucial features of these operators. Moreover, we present a step by step mechanism to solve MADM problem under bipolar fuzzy dynamic aggregation operators. In addition, these new techniques are successfully applied for the selection of the most promising emerging technology for enterprise integration. Finally, a comparative study is conducted to show the validity and practicability of the proposed techniques in comparison to existing methods.

Abstract Angiogenesis is crucial for tissue engineering, wound healing, and regenerative medicine. Nanomaterials constructed based on specific goals can be employed to activate endogenous growth factor‐related signaling. In this study, based on the conventional single‐stranded DNA self‐assembly into tetrahedral framework nucleic acids (tFNAs), the Apt02 nucleic acid aptamer and dimethyloxallyl glycine (DMOG) small molecule are integrated into a complex via a template‐based click chemistry reaction and toehold‐mediated strand displacement reaction. Thus, being able to simulate the VEGF (vascular endothelial growth factor) function and stabilize HIF (hypoxia‐inducible factor), a functional whole is constructed and applied to angiogenesis. Cellular studies demonstrate that the tFNAs‐Apt02 complex (TAC) has a conspicuous affinity to human umbilical vein endothelial cells (HUVECs). Further incubation with DMOG yields the tFNAs‐Apt02‐DMOG complex (TACD), which promotes VEGF secretion, in vitro blood vessel formation, sprouting, and migration of HUVECs. Additionally, TACD enhances angiogenesis by upregulating the VEGF/VEGFR and HIF signaling pathways. Moreover, in a diabetic mouse skin defect repair process, TACD increases blood vessel formation and collagen deposition, therefore accelerating wound healing. The novel strategy simulating VEGF and stabilizing HIF promotes blood‐vessel formation in vivo and in vitro and has the potential for broad applications in the vascularization field.

This research paper proposes a novel approach for constructing substitution boxes (S-boxes) over Gaussian integers, which are complex numbers with integer coefficients. The proposed method is based on the properties of the Gaussian integers and their arithmetic operations and ensures the S-boxes exhibit strong cryptographic properties. Furthermore, the paper demonstrates how these S-boxes can be utilized for image encryption through a substitution-permutation network (SPN) over Gaussian integers. The SPN involves iteratively applying the S-box and a permutation layer to the input image, which effectively scrambles the image data. Experimental results show that the proposed method achieves high security and robustness against various attacks while providing efficient encryption and decryption performance. This research thus provides a promising avenue for developing secure image encryption schemes based on Gaussian integers.

First, we will go through the theory behind the Eisenstein field (EF) and its extension field. In contrast, we provide a detailed framework for building BCH codes over the EF in the second stage. BCH codes over the EF are decoded using the Berlekamp-Massey algorithm (BMA) in this article. We investigate the error-correcting capabilities of these codes and provide expressions for minimal distance. We provide researchers and engineers creating and implementing robust error-correcting codes for digital communication systems with detailed information on building, decoding and performance assessment.

Canada is one of the main petroleum producers in the world. Through its oil sands exploitation, a viscous bitumen mixed with sand, water, and clay is being produced. This bitumen is so viscous that approximatively 20%–30% of diluent needs to be added to ease transportation, resulting in a mixture called diluted bitumen (dilbit). The transport of dilbit through North America comes with a potential risk for oil spills in freshwater ecosystems at any time of the year. In this study, a mesoscale spill tank was used to study dilbit spills in freshwater to understand the effect of cold (winter-like) vs. warmer (spring- and fall-like) water temperatures on its natural weathering and their toxicity to fathead minnow (Pimephales promelas) embryos. Water samples were collected weekly during two consecutive 35-day experiments ran at either 2 or 15 °C. Each week, fish larvae were exposed for 7 days, and water analysis was performed. Chemical analysis showed that the volatile organic compound, total organic carbon, and polycyclic aromatic hydrocarbon concentrations decreased in both experiments with time, while fish larvae exposed to both temperature settings yielded increased abnormalities, EROD activity, CYP1A, and glutathione S-transferase mRNA expression levels, and decreased heart rate. Importantly, there were no major differences between the temperature regimes on dilbit weathering, highlighting that if a spill occurs in colder waters, it would be equally toxic to organisms. This work provides new data on the potential risk of oil spill for use during response planning and modelling.

Big data pertains to extensive and intricate compilations of information that necessitate the implementation of proficient and cost-effective evaluation and analysis tools to derive insights and support decision making. The Fermatean fuzzy set theory possesses remarkable capability in capturing imprecision due to its capacity to accommodate complex and ambiguous problem descriptions. This paper presents the study of the concepts of dynamic ordered weighted aggregation operators in the context of Fermatean fuzzy environment. In numerous practical decision making scenarios, the term "dynamic" frequently denotes the capability of obtaining decision-relevant data at various time intervals. In this study, we introduce two novel aggregation operators: Fermatean fuzzy dynamic ordered weighted averaging and geometric operators. We investigate the attributes of these operators in detail, offering a comprehensive description of their salient features. We present a step-by-step mathematical algorithm for decision making scenarios in the context of proposed methodologies. In addition, we highlight the significance of these approaches by presenting the solution to the decision making problem and determining the most effective big data analytics platform for YouTube data analysis. Finally, we perform a thorough comparative analysis to assess the effectiveness of the suggested approaches in comparison to a variety of existing techniques.

Road traffic accidents (RTAs) pose a significant hazard to the security of the general public, especially in developing nations. A daily average of more than three thousand fatalities is recorded worldwide, rating it as the second most prevalent cause of death among people aged 5-29. Precise and reliable decisionmaking techniques are essential for identifying the most effective approach to mitigate road traffic incidents. This research endeavors to investigate this specific concern. The Fermatean fuzzy set (FFS) is a strong and efficient method for addressing ambiguity, particularly when the concept of Pythagorean fuzzy set fails to provide a solution. This research presents two innovative aggregation operators: the Fermatean fuzzy ordered weighted averaging (FFOWA) operator and the Fermatean fuzzy dynamic ordered weighted geometric (FFOWG) operator. The salient characteristics of these operators are discussed and important exceptional scenarios are thoroughly delineated. Furthermore, by implementing the suggested operators, we develop a systematic approach to handle multiple attribute decisionmaking (MADM) scenarios that involve Fermatean fuzzy (FF) data. In order to show the viability of the developed method, we provide a numerical illustration encompassing the determination of the most effective approach to alleviate road traffic accidents. Lastly, we conduct a comparative evaluation of the proposed approach in relation to a number of established methodologies.

This article introduced a new generalized RSA crypto-system based on $ 2n $ prime numbers called generalized RSA (GRSA). This is a modern technique to provide supreme security for the computer world by factoring the variable$ N $, where its analysis process has become much easier nowadays with the development of tools and equipment. $ 2n $ primes (prime numbers) are used in the GRSA crypto-system to provide security over the network system. This includes encryption, key generation, and decryption. In this method we used $ 2n $ primes which are not easily broken, $ 2n $ primes are not comfortably demented. This method provides greater performance and fidelity over the network system.

Abstract The isometry in crisp graph theory is a well-known fact. But, isometry under a fuzzy environment was developed recently and studied many facts. In a m-polar fuzzy graph, we have to think m components for each node and edge. Since, in our consideration, we consider m components for each nodes as well as edges, therefore we can not handle this type of situation using fuzzy model as their is a single components for this concept. Again, we can not apply bipolar or intuitionistic fuzzy graph model as each edges or nodes have just two components. Thus, these mPFG models give more efficient fuzziness results than other fuzzy model. Also, it is very interesting to develop and analyze such types of mPFGs with examples and related theorems. Considering all those things together, we have presented isometry under a m-polar fuzzy environment. In this paper, we have discussed the isometric m-polar fuzzy graph along with many exciting facts about it. Metric space properties have also been implemented on m-polar fuzzy isometric graph. We also have initiated a generalized fuzzy graph, namely antipodal m-polar fuzzy graphs, along with several issues. The degree of it is also presented along with edge regularity properties. We also give a relation between m-polar fuzzy antipodal graphs and their underlying crisp graphs. Its properties have also been discussed on m-polar fuzzy odd as well as even cycles, complete graphs, etc. Finally, a real-life application on a road network system in a m-polar fuzzy environment using the $$\mu$$ μ -distance concept is also presented.

Fuzzy topological indices are getting attention these days due to their vast applications in daily life. In crisp case, topological indices are beneficial in chemical graph theory but as far as fuzzy graph theory is concerned, fuzzy topological indices are useful in identifying human trafficking, and multi-criteria decision-making environments. In this paper, we have computed the fuzzy topological indices such as the first and second fuzzy Zagreb indices, Randic index, and Harmonic index for the $ Pz_{n} $ pizza graph. We have found generalized results for the above-mentioned structure.

The quantale module introduced by Abramsky and Vickers, engaged a large number of researchers. This research article focuses the combined behavior of rough set, soft set and an algebraic structure quantale module with the left action. In fact, the paper reflects the generalization of rough soft sets. This combined effect is totally dependent on soft binary relation including aftersets and foresets. Different soft substructures in quantale modules are defined. The characterizations of soft substructures in quantale modules based on soft binary relation are presented. Further, in quantale modules, we define soft compatible and soft complete relations in terms of aftersets and foresets. Furthermore, we use soft compatible and soft complete relations to approximate soft substructures of quantale modules and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough soft quantale modules. Additionally, we describe the algebraic relationships between the upper (lower) approximations of soft substructures of quantale modules and the upper (lower) approximations of their homomorphic images using the concept of soft quantale module homomorphism.

In this work, we will examine the concept of intuitionistic fuzzy k-ideals in the context of right k-weakly regular hemirings. We will investigate the properties of these ideals and how they relate to other concepts such as fuzzy prime k-ideals, intuitionistic fuzzy prime k-ideals, intuitionistic fuzzy right pure k-ideals, and purely prime intuitionistic fuzzy k-ideals in hemirings. We will also explore how the regularity of a k-weakly regular hemiring can be characterized through its intuitionistic fuzzy k-ideals.

With the development of fiber-reinforced cement composites, the diversity and complexity of application scenarios require enhanced strength and ductility and tough materials in practical engineering. To explore the effects of different water-binder ratios and fiber contents on the fluidity, bending resistance, tensile properties, fracture toughness, and fracture behavior of polyvinyl alcohol (PVA) fiber cement composites, several groups of high ductility test blocks (PVA-engineering cementitious composites (ECC)) with different mixing ratios were designed in this study. Based on the expansion degree, the mechanical experimental data, and the electron microscopy scanning image results, K-value analysis was performed on the strain hardening strength criterion. The effect of the water–binder ratio and the fiber dosing on the PVA-ECC material was determined. Results show that the greater the water-binder ratio is, the better the fluidity of the ECC matrix is. In the same cement system and at the same water-binder ratio, the fluidity of the ECC paste gradually deteriorates with the increase of the fiber content. The water-binder ratio significantly affects the flexural tensile strength of the composite. The flexural and tensile strengths of the PVA-ECC gradually increase as the water-binder ratio decreases, but the ductility gradually decreases. The water-binder ratio of the substrate directly influences the damage behavior of the fibers within the substrate. With the gradual increase of the water-binder ratio, the fiber at the crack interface gradually changes from pull-out morphology to fracture morphology. The strain capacity and the multi-crack cracking performance decrease. To achieve improved working performance in the actual project, the matrix water-binder ratio should be controlled at approximately 0.45, and the PVA fiber dose of 1.7% is optimal. This study can provide a good reference for the optimization of practical engineering components.

Planarity of crisp graphs is a well-established field, whereas planarity within a fuzzy framework has seen recent development and extensive exploration. In an $m$ -polar fuzzy graph ( $m$ PFG), each node and edge is associated with $m$ -components, connected through minimal relationships. However, if one desires to incorporate maximum, average, or other intermediate relationships between nodes and edges, the $m$ PFG concept becomes inadequate as in the $m$ -polar fuzzy model, only minimum relation is considered. To address this limitation, a generalized model of $m$ PFG is introduced in this article, allowing for a broader range of relationships to be considered simultaneously. This paper also discusses the properties of generalized $m$ -polar fuzzy environments and generalized $m$ -polar fuzzy graphs ( $\text{G}m$ PFGs), highlighting their isomorphism. Several significant findings and insights are presented in this paper. The article delves into the properties and characteristics of generalized $m$ -polar fuzzy planar graphs ( $\text{G}m$ PFPGs) and explores various intriguing aspects related to them. Additionally, a novel concept of a generalized $m$ -polar fuzzy dual graph ( $\text{G}m$ PFDG) is introduced, derived from $\text{G}m$ PFPGs. The paper establishes a relationship between the dual of a $\text{G}m$ PFG and $\text{G}m$ PFG, examining their properties in the context of dual $\text{G}m$ PFPGs. Lastly, the article discusses an illustrative example of a social group network problem assessing the group’s activity based on attributes such as cooperation, team spirit, awareness, controlling power, good behaviour, and creativity.

Offshore salmon aquaculture is a growing industry that faces challenges such as sea lice infestations and varying environmental conditions, necessitating the development of new monitoring systems to improve fish welfare and sustainability. In this paper, we propose and test a machine learning based method for underwater detection and localisation using multibeam echosounders (MBES) in fish farming applications. We demonstrate a three-stage process involving data acquisition, pre-processing, and object detection. We then compare the performance of four different vision based deep learning object detection algorithms in different signal-to-noise scenarios by artificially adding noise to the pre-beamformed signals. This method successfully detects fish in MBES images, which has potential applications in optimising feeding schedules, behaviour analysis, and fish health monitoring. Furthermore, this method holds potential for the detection and tracking of other objects within fish farms, such as cages and mooring lines. This study paves the way for further development of MBES data being used as a non-invasive and automated monitoring method in aquaculture.

The study of statistical distributions in a complex variable is one of the most vibrant areas of research. The complex analogue of many distributions has been studied. This article introduces the complex analogue of Binomial distribution and Negative Binomial distribution and studies certain geometrical properties of these analogues. It comprises the study of analytic functions defined by using the complex versions of Binomial distribution and Negative Binomial distribution functions. It includes the problems of finding the lower bounds of real parts of certain ratios of partial sums to the infinite series sums for these analytic functions. Such lower bounds are determined for the said analytic functions, for their first derivatives and for the Alexander transformation of these analytic functions.

Sustainable energy management is an inexpensive approach for improved energy use. However, the research used does not focus on cutting-edge technology possibilities in an Internet of things (IoT). This paper includes the needs for today’s distributed generation, households, and industries in proposing smart resource management deep learning model. A deep learning architecture of power management (DLA-PM) is presented in this article. It predicts future power consumption for a short period and provides effective communication between power distributors and customers. To keep power consumption and supply constant, mobile devices are linked to a universal IoT cloud server connected to the intelligent grids in the proposed design. An effective brief forecast decision-making method is followed by various preprocessing strategies to deal with electrical data. It conducts extensive tests with RMSE reduced by 0.08 for both residential and business data sources. Significant strengths include refined device-based, real-time energy administration via a shared cloud-based server data monitoring system, optimized selection of standardization technology, a new energy prediction framework, a learning process with decreased time, and lower error rates. In the proposed architecture, mobile devices link to a universal IoT cloud server communicating with the corresponding intelligent grids such that the power consumption and supply phenomena continually continue. It utilizes many preprocessing strategies to cope with the diversity of electrical data, follows an effective short prediction decision-making method, and executes it using resources. For residential and business data sources, it runs comprehensive trials with RMSE lowered by 0.08.

In this paper, the notion of picture fuzzy sub-hyperspace of a hyper vector space is introduced and some related results are investigated on the basis of some basic operations (intersection, union, Cartesian product etc.) on picture fuzzy sets. The concept of picture fuzzy linear transformation with respect to some picture fuzzy sub-hyperspace is initiated here and some important results are studied in this regard. It is shown that with respect to some pre-assumed picture fuzzy sub-hyperspace, linear combination of two picture fuzzy linear transformations is a picture fuzzy linear transformation, composition of two picture fuzzy linear transformations is a picture fuzzy linear transformation and inverse of a bijective picture fuzzy linear transformation is a picture fuzzy linear transformation. The effect of good linear transformation on picture fuzzy sub-hyperspaces is discussed here. It is shown that the image of a picture fuzzy sub-hyperspace is a picture fuzzy sub-hyperspace under bijective good linear transformation and the inverse image of a picture fuzzy sub-hyperspace is a picture fuzzy sub-hyperspace under good linear transformation. Some important results on picture fuzzy sub-hyperspaces in the light of (θ,ϕ,ψ)-cut of picture fuzzy set are studied here. Finally, an application of picture fuzzy sub-hyperspace conditions in decision making problem is presented here.

In this study, we investigate a possible relationship between fuzzy differential subordination and the theory of geometric functions. First, using the Al-Oboudi differential operator and the Babalola convolution operator, we establish the new operator BSα,λm,t:An→An in the open unit disc U. The second step is to develop fuzzy differential subordination for the operator BSα,λm,t. By considering linear transformations of the operator BSα,λm,t, we define a new fuzzy class of analytic functions in U which we denote by Tϝλ,t(m,α,δ). Several innovative results are found using the concept of fuzzy differential subordination and the operator BSα,λm,t for the function f in the class Tϝλ,t(m,α,δ). In addition, we explore a number of examples and corollaries to illustrate the implications of our key findings. Finally, we highlight several established results to demonstrate the connections between our work and existing studies.

A complex picture fuzzy set (Com-PFS) is a motivating tool for more precisely interpreting fuzzy notions. Recently, all extensions of complex fuzzy graphs (Com-FGs) have become a growing research topic as they handle ambiguous situations more explicitly than complex intuitionistic fuzzy graphs (Comp-IFG) and picture fuzzy graphs (PFG). The primary goal of this study is to demonstrate the foundation of Com-PFG due to the drawback of the complex neutral membership function in Com-IFG. This paper introduces the concept of Com-PFGs and explains many of the approaches to their development. A Com-PFG has three complex membership functions. We define the order, size, degree of vertex, and total degree of vertex in Com-PFGs. We elaborate on primary operations including: complement, join, union, Cartesian product, direct product, and composition of Com-PFG. Finally, we discuss its use in decision-making problems.

Gut microbiome is the most direct external environment of human body, which plays a vital role in maintaining human health. Gut microbiome maintains the homeostasis of the human immune system, which can coexist with the host and affect the nutrition, metabolism and immune function. Gut microbiome makes a mutual connection with the nervous system through the immune and endocrine systems, namely the "microbe⁃gut⁃brain" axis. Gut microbiome disorders can cause abnormal immune responses in the nervous system and the periphery, participating in the pathogenesis of autoimmune diseases. This article reviews the research progress of gut microbiome in multiple sclerosis (MS), neuromyelitis optica spectrum disorders (NMOSDs), autoimmune encephalitis (AE), myasthenia gravis (MG), Guillain⁃Barré syndrome (GBS) and other classic autoimmune diseases of the nervous system.

$(\alpha,\beta)$ -Pythagorean fuzzy set is a very efficient way of dealing with uncertainty. In this article, we have introduced the notions of $(\alpha,\beta)$ - Pythagorean fuzzy subring and $(\alpha,\beta)$ - Pythagorean fuzzy ideal of a ring. Further, we have briefly described various results related to it. Also, we have discussed the level subring of an $(\alpha,\beta)$ - Pythagorean fuzzy subring. Moreover, we have studied the direct product and ring homomorphism of $(\alpha,\beta)$ - Pythagorean fuzzy subrings.

Spam is any form of annoying and unsought digital communication sent in bulk and may contain offensive content feasting viruses and cyber-attacks. The voluminous increase in spam has necessitated developing more reliable and vigorous artificial intelligence-based anti-spam filters. Besides text, an email sometimes contains multimedia content such as audio, video, and images. However, text-centric email spam filtering employing text classification techniques remains today's preferred choice. In this paper, we show that text pre-processing techniques nullify the detection of malicious contents in an obscure communication framework. We use Spamassassin corpus with and without text pre-processing and examined it using machine learning (ML) and deep learning (DL) algorithms to classify these as ham or spam emails. The proposed DL-based approach consistently outperforms ML models. In the first stage, using pre-processing techniques, the long-short-term memory (LSTM) model achieves the highest results of 93.46% precision, 96.81% recall, and 95% F1-score. In the second stage, without using pre-processing techniques, LSTM achieves the best results of 95.26% precision, 97.18% recall, and 96% F1-score. Results show the supremacy of DL algorithms over the standard ones in filtering spam. However, the effects are unsatisfactory for detecting encrypted communication for both forms of ML algorithms.

A complex fuzzy set (CFS) is a generalization of a fuzzy set (FS) in which a limit of degrees occurs on the complex plane with unit disc. The averaging operators are a key part of turning all the data into one value. Dombi operators have exceptional flexibility with operating factors, and they are particularly efficient in decision-making problems. In this paper, we establish a complex dombi fuzzy graph (CDFG). We implement dombi operators on CFSs to extend graph nomenclature. We define the complement of CDFG with an example. The idea of self-complementary in CDFG is discussed. The concepts of homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism of two CDFGs are discussed. We define regular and entirely regular graphs with sufficient elaboration and examine their key properties. Furthermore, significant characteristics are used to explain the edge regularity of CDFG. Lastly, we establish an application of CDFG in decision making problems.

Fuzzy topological indices are one of the accomplished mathematical approaches for numerous technology, engineering, and real-world problems such as telecommunications, social networking, traffic light controls, marine, neural networks, Internet routing, and wireless sensor network (Muneera et al. (2021)). This manuscript comprises the study of a particular class of graphs known as qCn snake graphs. Some innovative results regarding fuzzy topological indices have been established. The major goal of the work is to introduce the notions of First Fuzzy Zagrab Index, Second Fuzzy Zagrab Index, Randic Fuzzy Zagrab Index, and Harmonic Fuzzy Zagrab Index of the qCn snake graph.

In order to improve the surface friction, wear and high temperature oxidation resistance of TC4 titanium alloy, NiCrCoAlY+20%(mass fraction) Cr3C2 mixed powder was selected as the cladding powder to prepare NiCrCoAlY-Cr3C2 composite coating on the surface of TC4 titanium alloy by using laser cladding technology. The microstructure and phase composition of the coating were analyzed by OM, SEM, XRD, EDS, etc.The microhardness of the coating was measured by HXD-1000TB tester. MMG-500 three-body wear tester and WS-G150 smart muffle furnace were used to test the friction, wear and high temperature oxidation resistance of the coating and substrate. The results show that the laser cladding technology can be used to prepare the good composite coating on the surface of TC4 titanium alloy without cracks and pores. The microstructure of the cladding zone is dense, mostly needle-like crystals and dendrites.The microstructure of the bonding zone is mainly composed of planar crystals, cellular crystals and dendrites, which generates a variety of products including the carbides, oxides and intermetallic compounds that can improve wear resistance and high temperature oxidation resistance. The maximum microhardness of the composite coating is 1344HV, which is about 3.8 times of the 350HV of the titanium alloy substrate.The friction factor of the composite coating is 0.2-0.3, which is significantly lower than the friction factor of the titanium alloy substrate of 0.6-0.7. Under the same conditions, the wear mass loss of the composite coating is 0.00060 g, which is 0.9% of that of 0.06508 g of titanium alloy substrate. After oxidation at 850℃ for 100 h, the oxidation mass gain of the composite coating is 6.01 mg·cm-2, which is about 24% of that of 25.10 mg·cm-2 of titanium alloy substrate. Laser cladding technology effectively improves the friction and wear performance and high temperature oxidation resistance of the TC4 titanium alloy surface.

Today, power generation from clean and renewable resources such as wind and solar is of great salience. Smart grid technology efficiently responds to the increasing demand for electric power. Intelligent monitoring, control, and maintenance of wind energy facilities are indispensable to increase the performance and efficiency of smart grids (SGs). Integration of state-of-the-art machine learning algorithms and vision sensor networks approaches pave the way toward enhancing the wind farms’ performance. The generating power in a wind turbine farm is the most critical parameter that should be measured accurately. Produced power is highly related to weather patterns, and a new farm in a near area is also likely to have similar energy generation. Therefore, accurate and perpetual prediction models of the existing wind farms can be led to develop new stations with lower costs. The paper aims to estimate the angular velocity of turbine blades using vision sensors and signal processing. The high wind in the wind farm can cause the camera to vibrate in successive frames, and the noise in the input images can also strengthen the problem. Thanks to couples of solid computer vision algorithms, including FAST (Features from Accelerated Segment Test), SIFT (Scale-Invariant Feature Transform), SURF (Speeded Up Robust Features), BF (Brute-Force), FLANN (Fast Library for Approximate Nearest Neighbors), AE (Autoencoder), and SVM (support vector machines), this paper accurately localizes the Hub and track the presence of the Blade in consecutive frames of a video stream. The simulation results show that determining the hub location and the blade presence in sequential frames results in an accurate estimation of wind turbine angular velocity with 95.36% accuracy.

Pythagorean fuzzy environment is the modern tool for handling uncertainty in many decisions making problems. In this paper, we represent the notion of Pythagorean fuzzy subgroup (PFSG) as a generalization of intuitionistic fuzzy subgroup. We investigate various properties of our proposed fuzzy subgroup. Also, we introduce Pythagorean fuzzy coset and Pythagorean fuzzy normal subgroup (PFNSG) with their properties. Further, we define the notion of Pythagorean fuzzy level subgroup and establish related properties of it. Finally, we discuss the effect of group homomorphism on Pythagorean fuzzy subgroup.

In this research article, the fundamental properties of complex anti-fuzzy subgroups as well as the influence of group homomorphisms on their characteristics are investigated. Both the necessary and sufficient conditions for a complex anti-fuzzy subgroup are defined; additionally, the image, inverse image and some vital primary features of complex anti-fuzzy subgroups are examined. Moreover, the homomorphic and isomorphic relations of complex anti-fuzzy subgroups under group homomorphism are discussed, and numerical examples for various scenarios to describe complex anti-fuzzy symmetric groups are provided. Finally, it is proven that every homomorphic image of a complex anti-fuzzy cyclic group is cyclic, but the converse may not be true.

Stable and reliable autonomous localization technology is fundamental for realizing autonomous driving. Localization systems based on global positioning system (GPS), cameras, LIDAR, etc., can be affected by building occlusion or drastic changes in the environment. These effects can degrade the localization accuracy and even cause the problem of localization failure. Localizing ground-penetrating radar (LGPR) as a new type of localization can rely only on robust subsurface information for autonomous localization. LGPR is mostly a 2D-2D registration process. This paper describes the LGPR as a slice-to-volume registration (SVR) problem and proposes an end-to-end TSVR-Net-based regression localization method. Firstly, the information of different dimensions in 3D data is used to ensure the high discriminative power of the data. Then the attention module is added to the design to make the network pay attention to important information and high discriminative regions while balancing the information weights of different dimensions. Eventually, it can directly regress to predict the current data location on the map. We designed several sets of experiments to verify the method’s effectiveness by a step-by-step analysis. The superiority of the proposed method over the current state-of-the-art LGPR method is also verified on five datasets. The experimental results show that both the deep learning method and the increase in dimensional information can improve the stability of the localization system. The proposed method exhibits excellent localization accuracy and better stability, providing a new concept to realize the stable and reliable real-time localization of ground-penetrating radar images.

Industrial Cyber-Physical Systems (CPSs) require flexible and tolerant communication networks to overcome commonly occurring security problems and denial-of-service such as links failure and networks congestion that might be due to direct or indirect network attacks. In this work, we take advantage of Software-defined networking (SDN) as an important networking paradigm that provide real-time fault resilience since it is capable of global network visibility and programmability. We consider OpenFlow as an SDN protocol that enables interaction between the SDN controller and forwarding plane of network devices. We employ multiple machine learning algorithms to enhance the decision making in the SDN controller. Integrating machine learning with network resilience solutions can effectively address the challenge of predicting and classifying network traffic and thus, providing real-time network resilience and higher security level. The aim is to address network resilience by proposing an intelligent recommender system that recommends paths in real-time based on predicting link failures and network congestions. We use statistical data of the network such as link propagation delay, the number of packets/bytes received and transmitted by each OpenFlow switch on a specific port. Different state-of-art machine learning models has been implemented such as logistic regression, K-nearest neighbors, support vector machine, and decision tree to train these models in normal state, links failure and congestion conditions. The models are evaluated on the Mininet emulation testbed and provide accuracies ranging from around 91–99% on the test data. The machine learning model with the highest accuracy is utilized in the intelligent recommender system of the SDN controller which helps in selecting resilient paths to achieve a better security and quality-of-service in the network. This real-time recommender system helps the controller to take reactive measures to improve network resilience and security by avoiding faulty paths during path discovery and establishment.

An (α,β)-Pythagorean fuzzy environment is an efficient tool for handling vagueness. In this paper, the notion of relative subgroup of a group is introduced. Using this concept, the (α,β)-Pythagorean fuzzy order of elements of groups in (α,β)-Pythagorean fuzzy subgroups is defined and examined various algebraic properties of it. A relation between (α,β)-Pythagorean fuzzy order of an element of a group in (α,β)-Pythagorean fuzzy subgroups and order of the group is established. The extension principle for (α,β)-Pythagorean fuzzy sets is introduced. The concept of (α,β)-Pythagorean fuzzy normalizer and (α,β)-Pythagorean fuzzy centralizer of (α,β)-Pythagorean fuzzy subgroups are developed. Further, (α,β)-Pythagorean fuzzy quotient group of an (α,β)-Pythagorean fuzzy subgroup is defined. Finally, an (α,β)-Pythagorean fuzzy version of Lagrange's theorem is proved.

By utilizing the concept of the q-fractional derivative operator and bi-close-to-convex functions, we define a new subclass of A, where the class A contains normalized analytic functions in the open unit disk E and is invariant or symmetric under rotation. First, using the Faber polynomial expansion (FPE) technique, we determine the lth coefficient bound for the functions contained within this class. We provide a further explanation for the first few coefficients of bi-close-to-convex functions defined by the q-fractional derivative. We also emphasize upon a few well-known outcomes of the major findings in this article.

The number of users of the Internet has been continuously rising, with an estimated 5.1 billion users in 2023, which comprises around 64.7% of the total world population. This indicates the rise of more connected devices to the network. On average, 30,000 websites are hacked daily, and nearly 64% of companies worldwide experience at least one type of cyberattack. As per IDC’s 2022 Ransomware study, two-thirds of global organizations were hit by a ransomware attack that year. This creates the desire for a more robust and evolutionary attack detection and recovery model. One aspect of the study is the bio-inspiration models. This is because of the natural ability of living organisms to withstand various odd circumstances and overcome them with an optimization strategy. In contrast to the limitations of machine learning models with the need for quality datasets and computational availability, bio-inspired models can perform in low computational environments, and their performances are designed to evolve naturally with time. This study concentrates on exploring the evolutionary defence mechanism in plants and understanding how plants react to any known external attacks and how the response mechanism changes to unknown attacks. This study also explores how regenerative models, such as salamander limb regeneration, could build a network recovery system where services could be automatically activated after a network attack, and data could be recovered automatically by the network after a ransomware-like attack. The performance of the proposed model is compared to open-source IDS Snort and data recovery systems such as Burp and Casandra.

In this paper, we define a subclass of starlike functions associated with the Van der Pol numbers. For this class, we derive structural formula, radius of starlikeness of order α, strong starlikeness, and some inclusion results. We also study radii problems for various classes of analytic functions. Furthermore, we investigate some coefficient-related problems which include the sharp initial coefficient bounds and sharp bounds on Hankel determinants of order two and three.