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The important feature of the multi-attribute decision-making (MADM) technique is to identify an ideal solution and aggregate collective cognitive fuzzy information of human opinion. To serve this purpose, we explore the concepts of the bipolar complex fuzzy set with positive and negative support terms. A few applications of the Hamy mean (HM) and Dual Hamy mean (DHM) models are also discussed to find out the relationship among input arguments or different preferences. For this, we derive a family of mathematical approaches by incorporating the theory of bipolar complex fuzzy information such as bipolar complex fuzzy Hamy mean (BCFHM), bipolar complex fuzzy weighted Hamy mean (BCFWHM), bipolar complex fuzzy Dual Hamy mean (BCFDHM), and bipolar complex fuzzy weighted Dual Hamy mean (BCFWDHM) operators. Derived mathematical approaches are more applicable and can express the influence of uncertain information due to the involvement of additional parameter values. Based on diagnosed research work and mathematical methodologies, we establish a decision algorithm for the MADM problem to resolve real-life dilemmas. An experimental case study demonstrates the compatibility of derived approaches and evaluates the investment policy's sustainability based on certain parameters. The advantages and consistency of the proposed research work are verified in the comparative study with various existing aggregation operators.

The exposure of human beings to various respiratory diseases has sparked an interest among scientists to propose and promote inhalable nanoparticle-based pharmaceutical products. This new drug delivery system will be an effective and prompt therapy for next-generation respiratory therapeutics. There are many available formulations on account of the treatments for lung diseases, i.e., oral, injectable, aerosol, nebulizer-based, etc. But, due to extended distribution and elimination, repeated intake, and complex systems of application, these treatments create overload on patients along with other expenses of daily life. Amid these treatments, inhalable nanoparticle-based dry powder formulations are considered superior owing to their simplicity, convenience of use, and long-term stability. This review aims to formulate an inhalable nanoparticle dry powder formulation to attain confined distribution of the remedy to the respiratory system. Dry powder formulations based on inhalable nanoparticles provide a novel and cutting-edge method of treating lung conditions. This novel drug delivery system is an improved treatment for lung disorders in terms of its efficacy and reduced dose requirement. Subsequently, the availability of this formulation will be an alternative option for patients to improve treatment compliance and, foremost, therapeutic outcomes in different lung ailments. The salient features of dry formulations that illustrate their uniqueness are deep penetration to lung tissues, enhanced deposition in lung regions, improved solubility, elevated bioavailability, targeted drug delivery, stability at storage, convenient to use, versatile and customizable formulation. This novel inhalable formulation is based on finely dried nanoparticles or freeze-dried particles. This formulation will contain an excessive amount of dried nanoparticles, and if it is combined with a beneficial tool, i.e., a spray, pump, or puffer, it will be a pleasant way to apply drugs directly to the lungs.

Energy Supplier Selection is vital for sustainable energy management. Optimal supplier choices reduce environmental impact and promote resource efficiency per green principles. However, A decision model for Energy Supplier Selection is crucial in making informed choices for sustainable and efficient energy management. A complex fuzzy set (CFS) is the generalization of the fuzzy set (FS). It is a vital tool to deal with uncertain situations, especially when an object is to be described as a part of a real-life scenario. CFS represents the belongingness of anything to a real-life system with the help of two terms. Furthermore, a rough set (RS) is another tool to reduce uncertainty using approximations. The primary goal of this article is to develop a technique for selecting energy suppliers based on multiple attributes. Complex fuzzy rough sets (CFRS) are created by first making a bridge between CFS and RS. CFRS is not any new theory but is obtained by applying the idea of the roughness of CFS. Hence, CFRS is the framework that deals with uncertainty more accurately than the CFS and RS. With the development of the CFRS, we also need the operators that should deal with the information in the form of the CFRS. So, complex fuzzy rough weighted averaging (CFRWA) and complex fuzzy rough weighted geometric (CFRWG) operators are developed to deal with the information in the form of complex fuzzy rough values (CFRVs). Some basic properties of these operators are discussed and verified. Finally, the developed operators are applied to the real-life problem of multi-attribute decision-making (MADM) by using the technique for order of preference by similarity to the ideal solution (TOPSIS) method.

Abstract Picture fuzzy set (PFS) is an expedient mathematical approach for interpreting imprecise and nebulous information, and the power Bonferroni mean (PBM) operator is a crucial generalization of the power average (PA) operator, and the Bonferroni mean (BM) operator. Based on the Aczel-Alsina (AA), operational principles of PFS, we expand the PBM operator to integrate PFVs and develop a few AOs, namely PF Aczel-Alsina PBM (PFAAPBM) operator, weighted PF Aczel-Alsina PBM (WPFAAPBM) operator, PF Aczel-Alsina PGBM (PFAAPGBM) operator, and weighted geometric PF Aczel-Alsina PBM (WGPFAAPBM) operators respectively. These newly suggested PF Aczel-Alsina PBM operators can detect the connections between the membership, abstinence, and non-membership functions, which also maintain the important characteristics of the PBM operator. After that, we analyze a few enticing characteristics along with the particular applications of the suggested operators. Based on our suggested technique, we built an illustrated numerical example for the selection of competent research scientists to cope with MADM issues under the framework of PFVs. Finally, we contrast a few of our suggested methodologies with other prevailing methods to determine the feasibility and legitimacy of our suggested strategies.

Abstract Background Childhood vaccination is widely recognized as the most effective means to prevent various diseases. However, a considerable amount of children still miss out on their vaccination schedules. Therefore, this study explores the reasons for defaulting from the expanded program on immunization in district Swat, Pakistan. Methods A qualitative phenomenological approach was used. Data collection took place from March to September 2022. Thirty-six in-depth interviews were conducted with participants who had defaulter children. The collected qualitative data were analysed thematically to identify key patterns and themes related to the reasons for defaulting from childhood vaccination schedules. Results Six themes emerged, i.e., illness of the defaulter child at the scheduled time, perceived side effects of the vaccination, factors related to caregivers, myths and misconceptions, vaccinators attitudes and crowed vaccination centres, as well as poor immunization service arrangements. Four subthemes arose related to caregivers, such as lack of clear understanding about completion of vaccination, least priority for child’s vaccination, cultural restriction on mothers, and the loss of vaccination card. Conclusion According to the study’s findings, caregivers have their own perceptions regarding the non-completion of their children’s vaccination schedule. The childhood immunization defaulting arises from various factors including child illness, Adverse Events Following Immunization (AEFIs) concerns, misconceptions, improper injection techniques, and negative vaccinator attitudes. The vaccination completion rate may be increased if the concerns of the caregivers are appropriately addressed.

The multi-attribute group decision-making (MAGDM) technique is a potent approach used to evaluate an appropriate optimal option under the system of various characteristics or attributes information. The aggregation operators (AOs) play a significant role in the aggregation process and fuse a large amount of uncertain information into a single set. In this article, dominant terminologies of t-spherical fuzzy sets apply to handle vague and ambiguous information related to human opinion. Some flexible operations of Einstein operations are also modified in the light of t-spherical fuzzy information. The power operators characterized relationships among various types of preference information. Keeping in mind the significance of discussed terminologies, we developed some Einstein mathematical approaches, including T-SF Einstein power-weighted average (T-SFEPWA) and T-SF Einstein power-weighted geometric (T-SFEPWG) operators. Some desirable characteristics and special cases are also demonstrated to reveal the reliability of developed approaches. An algorithm for the MAGDM problem is also established to resolve different real-life situations. To show the consistency and effectiveness of the proposed approaches, the author illustrates a numerical example to choose an appropriate data analysis tool under the system of T-SF information. Additionally, a comprehensive comparison method verifies the validity and feasibility of diagnosed mathematical approaches with existing AOs in the literature.

Hemoglobin is the iron containing protein in red blood cells which carries oxygen from lungs to rest of the body tissues. Accurate measurement of hemoglobin is essential for diagnosing anemia, a condition characterized by a deficiency of red blood cells. This measurement is particularly vital before initiating blood transfusions for thalassemia patients. Non-invasive estimation of hemoglobin levels can be achieved through photoplethysmography (PPG)-based methods. PPG is an optical method to measure blood volume changes in successive heart beats. PPG signals can be obtained from fingertip videos using a light source and a photodetector. SmartphonePPG utilizes a smartphone’s flashlight as a light source and its camera as a photodetector to acquire PPG signals, offering an affordable and portable point-of-care tool. Despite the ubiquity of smartphones, signals from their cameras often contain noise, making feature selection from PPG characteristics challenging. While PPG-based methods are invaluable, the lack of real-world datasets poses a significant challenge in maximizing the benefits of PPG technology. In this paper, we introduce a dataset comprising 1-minute fingertip video recordings from 150 anemic patients, obtained using a smartphone’s camera. The dataset, publicly accessible for research purposes (https://forms.gle/LB4qn81ZMqEuy3V27), covers an age range of 6 months to 32 years, with diverse hemoglobin values (4.3 gm/dL - 12.4 gm/dL). Utilizing this dataset, we propose a deep learning-based technique employing the ResNet-18 architecture to estimate hemoglobin levels. This approach eliminates the need for manual feature extraction and selection from PPG signals, overcoming a limitation in existing smartphone PPG-based hemoglobin estimation systems. Our model achieves a hemoglobin level estimation with an RMSE of 0.81-1.39 when compared with the gold standard laboratory method, Complete Blood Count (CBC) test reports. In contrast, HemaApp, a state-of-the-art research utilizing a machine learning-based classifier (SVM), yields an RMSE of 1.7 on our dataset. The accuracy and simplicity of our model position it as a promising alternative to existing non-invasive hemoglobin level estimation methods.

The assessment of performance in agricultural education practice is an important issue because it concerns the quality and effectiveness of agricultural education. This evaluation requires effective assessment methods. Interval-valued intuitionistic fuzzy set (IVIFS) is a powerful extension of fuzzy sets and intuitionistic fuzzy sets, conceived to handle uncertainty and vagueness more effectively in agricultural education practice assessment performance. A comprehensive exploration of interval-valued intuitionistic fuzzy (IVIF) information offers some flexible methods for assessment of the performance of agricultural education practice. This article identifies the relationship among input arguments with the help of Hamy mean aggregation models. In order to avail smooth approximated results during the aggregation process, some prominent operations of Aczel Alsina aggregation operators have also been adopted in light of an IVIF theory. The robustness of this article is to develop a family of new mathematical strategies based on IVIF information, namely IVIF Hamy mean (IVIFHM), IVIF weighted Hamy mean (IVIFWHM), IVIF Dual Hamy mean (IVIFDHM) and IVIF weighted Dual Hamy mean (IVIFWDHM) operators. Some dominant properties of diagnosed aggregation operators are also discussed to show their validity and effectiveness. Moreover, the decision algorithm of the multi-attribute decision-making (MAMD) problem is also adopted to reveal the versatility and adaptability of IVIF contexts. A case study of agricultural education practice assessment performance is also illustrated to showcase the practicability of derived approaches. The advantages and supremacy of invented research work are verified with a comparative study of prevailing research work that exists in the literature.

Multi-Attribute Decision Making (MADM) is a powerful tool for navigating complex decision problems by systematically considering multiple criteria and alternatives. This method is widely used in various fields such as business, engineering, finance, and public policy, where decisions involve considering multiple conflicting objectives. An interval-valued intuitionistic fuzzy set is a more flexible mathematical model used to aggregate vague type and redundant information into a single set. By exploring the robustness of Aczel Alsina aggregation operators, we deduce an effective mathematical approach for handling ambiguous information of human opinion. To express the relationship among input arguments or attribute information, we study a feasible theory of Hamy mean (HM) operators. This article presents some dominant mathematical approaches in the light of interval-valued intuitionistic fuzzy (IVIF) information with Aczel Alsina operations including IVIF Aczel Alsina HM (IVIFAAHM), IVIF Aczel Alsina weighted HM (IVIFAAWHM), IVIF Aczel Alsina Dual HM (IVIFAADHM) and IVIF Aczel Alsina weighted Dual HM (IVIFAAWDHM) operators. To prove the validity and effectiveness of derived approaches, some prominent characteristics are also illustrated. A decision algorithm of the MADM technique is also established to resolve complicated real-life applications and amplifications. With the help of numerical examples, we show the compatibility of diagnosed mathematical approaches. Finally, the influence study and comparison technique also verify the consistency of pioneered approaches by contrasting the aggregated outcomes of previous operators that exist in the literature.

Abstract A T-spherical uncertain linguistic set (TSULS) is not only an expanded form of the T-spherical fuzzy set and the uncertain linguistic set but can also integrate the quantitative judging ideas and qualitative assessing information of decision-makers. For the description of complex and uncertain assessment data, TSULS is a powerful tool for the precise description and reliable processing of information data. However, the existing multi-attribute border approximation area comparison (MABAC) method has not been studied in TSULS. Thus, the goal of this paper is to extend and improve the MABAC method to tackle group decision-making problems with completely unknown weight information in the TSUL context. First, the cross-entropy measure and the interactive operation laws for the TSUL numbers are defined, respectively. Then, the two interactive aggregation operators for TSUL numbers are developed, namely T-spherical uncertain linguistic interactive weighted averaging and T-spherical uncertain linguistic interactive weighted geometric operators. Their effective properties and some special cases are also investigated. Subsequently, a new TSULMAGDM model considering the DM’s behavioral preference and psychology is built by integrating the interactive aggregation operators, the cross-entropy measure, prospect theory, and the MABAC method. To explore the effectiveness and practicability of the proposed model, an illustrative example of Sustainable Waste Clothing Recycling Partner selection is presented, and the results show that the optimal solution is h 3. Finally, the reliable, valid, and generalized nature of the method is further verified through sensitivity analysis and comparative studies with existing methods.

The multi-attribute decision-making (MADM) technique is a dominant process for resolving genuine real-life applications and investigating an ideal solution by considering appropriate criteria or attributes. The operational laws of Schweizer-Sklar t-norms and t-conorms are more feasible aggregation operators to serve this purpose. The prioritized aggregation operators also capture single-term aggregated information from given evidence or collected data. In this article, we explore the theory of the q-rung orthopair fuzzy (q-ROF) information to handle awkward and uncertain information of human opinion. Motivated by the significance of the Schweizer-Sklar t-norms and prioritized aggregation operators, we derive a family of mathematical approaches for q-rung orthopair fuzzy information, including q-rung orthopair fuzzy Schweizer-Sklar prioritized average (q-ROFSSPA), q-rung orthopair fuzzy Schweizer-Sklar prioritized weighted average (q-ROFSSPWA), q-rung orthopair fuzzy Schweizer-Sklar prioritized geometric (q-ROFSSPG) and q-rung orthopair fuzzy Schweizer-Sklar prioritized weighted geometric (q-ROFSSPWG) operators. Some notable properties and characteristics are also explored to show the applicability of developed approaches. An application for improving the economic growth of the agriculture sector and a decision algorithm is also discussed under the q-rung orthopair fuzzy environment. With the help of invented mathematical approaches, we resolved a numerical example to choose a suitable crop under reliable characteristics or attributes. To show the reliability and applicability of initiated methodologies, we demonstrate a comparison technique to contrast the results of pioneered aggregation operators with prevailing strategies in the literature.

The multi-attribute group decision-making (MAGDM) problem is used to evaluate suitable options based on specific attributes or characteristics of an object. The potential of the MAGDM problem is demonstrated in every field of life, like artificial intelligence, social and environmental science, networking, medical diagnosis, and many other domains. The essential components of the MAGDM technique are aggregation operators (AOs), which several mathematicians develop under the system of different fuzzy domains. In this article, we express the notion of an interval-valued t-spherical fuzzy (IVT-SF) set (IVT-SFS), which is an expanded form of an intuitionistic fuzzy set and picture fuzzy set with four characteristics of human opinions. An IVT-SFS is a well-known aggregation model that can deal with unpredictable and redundant information about human opinions. To mitigate the influence of redundant information, we illustrate some robust operations of Aczel Alsina aggregation tools in light of IVT-SF information. Power operators are used to reduce the impact of redundant information impact and define correlation among different input arguments. By combining two different concepts like Aczel Alsina aggregation tools and power operators, we developed a class of new approaches based on IVT-SF information, namely IVT-SF Aczel Alsina power weighted average (IVT-SFAAPWA) and IVT-SF Aczel Alsina power weighted geometric (IVT-SFAAPWG) operators. In order to illustrate the effectiveness of the proposed approaches, some notable characteristics and properties are also presented. To resolve different real-life applications, we established an algorithm for the MAGDM problem in light of IVTSF information. We illustrate a numerical example to evaluate an appropriate optimal option for digital devices in the healthcare system. The advantages and consistency of derived approaches are verified by comparing the findings of existing methodologies with currently discussed AOs.

IoT-based remote health monitoring is a promising technology to support patients who are unable to travel to medical facilities. Due to the sensitivity of health data, it is important to secure it against all possible threats. While a great deal of work has been done to secure IoT device-cloud communication and health records on the cloud, insider attacks remain a significant challenge. Malicious insiders may tamper, steal or change patients’ health data, which results in a loss of patient trust in these systems. Audit logs in the cloud, which may point to illegal data access, may also be erased or forged by malicious insiders as they tend to have technical knowledge and privileged access to the system. Thus, in this work, we propose a Cloud Access Security Broker (CASB) model that (a) logs every action performed on user data and (b) secures those logs by placing them in a private blockchain that is viewable by the data owners (i.e., patients). Patients can query the blockchain, track their data’s movement, and be alerted if their data has been accessed by an administrator or moved outside the cloud storage. In this work, we practically implement a web application that receives health data from patients, a CASB that securely stores the records in the cloud, and integrate a private blockchain that immediately logs all actions happening in the backend of the web application and CASB. We evaluate the system’s security and performance under varying numbers of patients and actions.

Social and economic factors, such as education, employment, social support, income, and community safety, can directly affect how well and long we live. Under the presence of the above factors, we easily look at health decisions, afford medical care and housing, manage stress, and so on. In this analysis, we derive the Choquet-integral aggregation operators based on Hamacher t-norm and t-conorm for complex Atanassov intuitionistic fuzzy (CAIF) such as CAIF Choquet-integral Hamacher averaging (CAIFCIHA), CAIF Choquet-integral Hamacher ordered averaging (CAIFCIHOA), CAIF Choquet-integral Hamacher geometric (CAIFCIHG), CAIF Choquet-integral Hamacher ordered geometric (CAIFCIHOG) operators and exposed their properties. Additionally, we discover the Technique for Order Preference by Similarity to the Ideal Solution “TOPSIS” technique under the consideration of the above-derived theory. Moreover, it is very famous and interesting to note that various unpredicted factors such as road, diesel prices, weather, and traffic conditions affect the cost of transportation. Therefore, decision-makers deal with vague and unreliable information to estimate the cost of transportation. To evaluate the above problem, we select a transportation problem with CAIF parameters, and for its evaluation, a simple and well-known computational technique is derived and illustrated. Finally, we compared our derived results with some prevailing results to show the worth and reliability of the exposed approaches.

Knowledge graph (KG) summarization facilitates efficient information retrieval for exploring complex structural data. For fast information retrieval, it requires processing on redundant data. However, it necessitates the completion of information in a summary graph. It also saves computational time during data retrieval, storage space, in-memory visualization, and preserving structure after summarization. State-of-the-art approaches summarize a given $KG$ by preserving its structure at the cost of information loss. Additionally, the approaches not preserving the underlying structure, compromise the summarization ratio by focusing only on the compression of specific regions. In this way, these approaches either miss preserving the original facts or the wrong prediction of inferred information. To solve these problems, we present a novel framework for generating a lossless summary by preserving the structure through super signatures and their corresponding corrections. The proposed approach summarizes only the naturally overlapped instances while maintaining its information and preserving the underlying Resource Description Framework $RDF$ graph. The resultant summary is composed of triples with positive, negative, and star corrections that are optimized by the smart calling of two novel functions namely $merge$ and $disperse$ . To evaluate the effectiveness of our proposed approach, we perform experiments on nine publicly available real-world knowledge graphs and obtain a better summarization ratio than state-of-the-art approaches by a margin of 10% to 30% with achieving its completeness, correctness, and compactness. In this way, the retrieval of common events and groups by queries is accelerated in the resultant graph.

Trajectory data, increasingly available due to location tracking technologies, holds immense potential for intelligent traffic management and urban planning. Traditional 'attractive region' mining methods often rely on density-based clustering, neglecting the inherent path information within trajectories. To address this, we propose a novel graph-based approach for attractive region discovery. By transforming trajectory data into graphs, we effectively leverage path and connectivity information for clustering with locality-sensitive hashing. Our study introduces the pARM, pgARM, and hgARM algorithms, demonstrating their superiority over GridDBScan through experiments on real-world datasets. We employ Davies–Bouldin metric and visualization techniques to highlight the robustness of our approach, especially for datasets with varied degree distributions. Although our method may have slightly longer processing times for smaller grid sizes, it achieves execution times comparable to GridDBScan for larger grids. We rigorously analyze performance variations within our algorithms using execution time, clustering coefficient, and modularity scores, providing guidance for their optimal application.

This article presents a novel study of spherical fuzzy sets (SFSs), a more comprehensive framework of intuitionistic fuzzy sets and picture fuzzy sets. The SFS allows the decision-makers (DMs) to cope with complicated and insufficient information during the aggregation process. The Heronian mean (HrM) model theory is also utilized to express correlation among different input arguments or characteristics. Recently, the theory of Aczel Alsina triangular norms gained a lot of attention from various research scholars and has many capabilities to provide smooth approximations during decision analysis. In this article, we developed some appropriate operations of Aczel Alsina t-norms and t-conorms in light of spherical fuzzy (SF) information. We develop new mathematical ways to look at SF data to keep clarity and sufficient information. These are the SF Aczel Alsina Heronian mean (SFAAHrM) and SF Aczel Alsina weighted Heronian mean (SFAAWHrM) operators. Furthermore, we also present a list of new strategies based on Aczel Alsina operations, such as SF Aczel Alsina geometric Heronian mean (SFAAGHrM) and SF Aczel Alsina weighted geometric Heronian mean (SFAAWGHrM) operators. Some notable properties are also characterized to show the validity and effectiveness of our derived mathematical approaches. Considering our derived strategies, an algorithm for the multiple attribute decision-making (MADM) problem is established to resolve complicated real-life applications. A numerical example presents the compatibility of derived approaches and provides a solid mechanism to improve the performance of educational institutes. A comparison technique is also demonstrated to show the applicability and consistency of diagnosed approaches by contrasting the findings of pioneered approaches with existing methodologies.

Abstract We compute the numerical solution of the Bratu’s boundary value problem (BVP) on a Banach space setting. To do this, we embed a Green’s function into a new two-step iteration scheme. After this, under some assumptions, we show that this new iterative scheme converges to a sought solution of the one-dimensional non-linear Bratu’s BVP. Furthermore, we show that the suggested new iterative scheme is essentially weak w 2 $w^{2}$ -stable in this setting. We perform some numerical computations and compare our findings with some other iterative schemes of the literature. Numerical results show that our new approach is numerically highly accurate and stable with respect to different set of parameters.

Abstract This manuscript proposes the concept of Schweizer–Sklar operational laws under the consideration of the complex interval-valued intuitionistic fuzzy (CIVIF) set theory, where the Schweizer–Sklar norms are the essential and valuable modification of many norms, such as algebraic, Hamacher, and Lukasiewicz norms. Moreover, keeping the dominancy of the presented laws, we derive the concept of CIVIF Schweizer–Sklar power averaging (CIVIFSSPA), CIVIF Schweizer–Sklar power ordered averaging (CIVIFSSPOA), CIVIF Schweizer–Sklar power geometric (CIVIFSSPG), and CIVIF Schweizer–Sklar power ordered geometric (CIVIFSSPOG) operators, which are the combination of the three different structures for evaluating three different problems. Further, some reliable and feasible properties and results for derived work are also invented. Additionally, we also illustrate an application, called multi-attribute decision-making (MADM) scenario for evaluating some real-world problems with the help of discovered operators for showing the reliability and stability of the evaluated operators. Finally, we compare our mentioned operators with various prevailing operators for enhancing the worth and stability of the evaluated approaches.

The Multi-attribute decision-making (MADM) approaches are utilized to aggregate ambiguous and imprecise information based on different aggregation operators (AOs). The aim of this article is to explore the notion of single-valued neutrosophic (SVN) set (SVNS), wich is the modified structure of an intuitionistic fuzzy sets and picture fuzzy sets. Some appropriate operations of Aczel Alsina tools under the system of SVN information are also presented. By using the theory of prioritization aggregation model, we developed a class of new approaches including SVN Aczel Alsina prioritized average (SVNAAPA) and SVN Aczel Alsina prioritized geometric (SVNAAPG) operators. We also presented a series of new methodologies in the light of SVN information such as SVN Aczel Alsina prioritized weighted average (SVNAAPWA), and SVN Aczel Alsina prioritized weighted geometric (SVNAAPWG) operators. To verify discussed aggregation approaches, we also presented some notabe characteristics. We established a MADM technique to solve complexities and difficulties during decision-making in our real-life problems. By utilizing a practical numerical example to select an appropriate research scientist for the vacant post of a public university. To find the validity and flexibility of our invented approaches, sensitive analysis, and comparative study by comparing the results of existing approaches with currently proposed aggregation techniques.

Data management and finding precise outcomes from large amounts of information are among the biggest challenges for scientists. The technique of multi-attribute group decision-making (MAGDM) is a valuable tool for investigating fuzzy data precisely. The key objective of the paper is to redefine the q-rung orthopair (q-RO) fuzzy set (FS) (q-ROFS) in the term of interval-valued and proposed new aggregation operators (AOs) based on the Aczel-Alsina (AA) t-norm (TN) and t-conorm (TCN) operations. The AA operational laws are a generalized form of existing TNs and TCNs and give more reliable results because they can fluctuate in their parametric values. The concept of interval-valued enlarges the space of membership degree (MD) and non-membership degree (NMD) for decision-makers. By taking qth power, the interval-valued q-ROFS (IV-q-ROFS) structure. The IV-q-ROFS can handle the uncertainty and vagueness in data, then interval-valued intuitionistic FS (IV-IFS) and interval-valued Pythagorean FS (PyFS) (IV-PyFS) and provide accurate results. The thought of power AOs (PAOs) makes the relationship between weight vectors and reduces the chances of uncertainty in aggregated results. By taking advantage of PAOs, this article is devoted to introducing the interval-valued q-ROF Aczel-Alsina power-weighted averaging (IV-q-ROFAAPWA) and interval-valued q-ROF Aczel-Alsina power-weighted geometric (IV-q-ROFAAPWG) operators. The fundamental axioms of AOs, idempotency, boundedness, and monotonicity, are also discussed. To illustrate the importance of suggested AOs, the real-life problem of electric car selection was solved by applying the MAGDM method using the proposed IV-q-ROFAAPWA and IV-q-ROFAAPWG operators. The comparison of proposed AOs with currently present AOs is also part of the article. We finally constructed solid conclusions.

Aggregation operators (AOs) are well-known and efficient mathematical tools that are utilized to overcome the impact of imprecise and vague information during the aggregation process. The theoretical concepts of Aczel Alsina aggregation expressions are an extension of triangular norms and become a hot research topic in the environment of the fuzzy framework. The power operators provide a smooth approximation and are used to mitigate the influence of redundant or insufficient information on the attributes or criteria. Some robust aggregation approaches are developed by combining two different theories, like power operators and Aczel Alsina aggregation tools. This article aims to explore the theory of picture fuzzy sets (PFSs), an extended version of fuzzy sets, and intuitionistic fuzzy sets. Some robust operations of Aczel Alsina aggregation tools are also present in light of the picture fuzzy environment. We established a class of new methodologies in the light of picture fuzzy information, including picture fuzzy Aczel Alsina power weighted average (PFAAPWA) and picture fuzzy Aczel Alsina power ordered weighted average (PFAAPOWA) operators. We also developed an appropriate approach like picture fuzzy Aczel Alsina power weighted geometric (PFAAPWG) and picture fuzzy Aczel Alsina power ordered weighted geometric (PFAAPOWG) operators. Notable properties and characteristics of proposed methodologies are also demonstrated. Our invented approaches not only aggregate complicated information but can clearly define interrelationships among several arguments. Moreover, we establish an algorithm for the multi-attribute group decision-making (MAGDM) problem to handle the impact of redundant and vague information on human opinions. Finally, we study an experimental case study to evaluate an appropriate optimal option from available options. To reveal consistency and effectiveness of developed approaches, influence study by changing various parametric values and comparative study by comparing results of existing approaches.

Boost converters are widely used in industry for many applications, such as electrical vehicles, wind energy systems, and photovoltaic energy systems, to step up the low voltages. Using the topology structure of the DC–DC boost circuit, this paper studied and designed a dual loop control method based on proportional integral controllers for improving the converter efficiency. The inner loop and outer loop controls of the traditional boost circuit are adopted in MATLAB/Simulink software to make the output of the system more stable. The input voltage is set to 24 V DC, and the desired output voltage varies from 36 to 48 V. Through simulation verification, the influence of a 1 kW sudden load connection by using a switch at a nominal output voltage of 48 V DC is studied, and the results show that it reduces the transient output voltage dips during the sudden load connection. Simulation analysis verifies the design scheme of the system, reduces the fluctuation in output voltage and power, reduces the output current ripple, minimizes the dip in voltage to a minimum possible value, and improves the dynamic characteristics and overall efficiency of the converter.

This article aims to introduce new aggregation operators (AOs) by assigning the positive real values known as priority degree among the strict priority levels. To Develop the complex T-spherical fuzzy (TSF) frank prioritized (CTSFFP) AOs, using the frank t-norm (FTN) and frank t-conorm (FTCN) operational laws, also explain sum, product, and power operations under complex TSF information. The TSF set framework has a superior structure for uncertain data handling than an existing intuitionistic fuzzy set (FS), Pythagorean FS (PyFS), q-rung orthopair FS (q-ROFS), picture FS (PFS), and spherical FS (SFS). Because the structure of the TSF set has the most generalized form of IFS, PyFS, q-ROFS, PFS, and SFS, it provides greater freedom to decision experts for handling information where these discussed sets fail to aggregate ambiguous details. Utilizing the idea of priority degree, proposed new AOs called CTSFFP weighted averaging (CTSFFPWA), CTSFFP ordered weighted averaging (CTSFFPOWA), CTSFFP hybrid weighted averaging (CTSFFPHWA), CTSFFP weighted geometric (CTSFFPWG), CTSFFP ordered weighted geometric (CTSFFPOWG), CTSFFP hybrid weighted geometric (CTSFFPHWG) operators. Some desirable properties of AOs, such as idempotency, monotonicity, and boundedness, are also discussed. To show the importance of proposed AOs, the real-life problem of multi-attribute decision-making (MADM) is solved with the help of developed CTSFFPWA and CTSFFPWG operators. To enhance the proposed AOs' superiority, compare the diagnosed theory with existing AOs and give conclusions.

Multiattribute decision making (MADM) approach is a well-known decision-making process utilized in a variety of fields such as solid waste management, renewable energy resources, air quality assurance, hotel location decision, sustainable supplier selection, partner recognition, green supplier enterprises, game theory, construction development authority, and weapon group target estimation. The aggregation operators (AOs) are essential components of the decision-making process and have a great capability to deal with ambiguous and unpredictable information in the different fields of fuzzy environments. In this article, we expressed the theory concepts of single-valued neutrosophic (SVN) sets (SVNS) and also characterized their basic operations. The power aggregation tools are allowed to input arguments to support each other among different arguments. Recently, Aczel–Alisna aggregation tools conquered great attention from several research scholars. We also exposed some reliable operations of Aczel–Alsina aggregation models under the consideration of SVN information. We established a series of new approaches, including the “single-valued neutrosophic Aczel–Alsina power weighted average” (SVNAAPWA) operator and “single-valued neutrosophic Aczel–Alsina power weighted geometric” (SVNAAPWG) operators. To show the effectiveness and compatibility of derived approaches, some prominent characteristics are also established. We constructed a MADM technique to solve an application of engineering and construction materials under consideration of our derived methodologies. An experimental case study is also presented to determine a suitable optimal option from a group of options. To find the flexibility of our proposed work, we provided a comparative study that compares the results of existing AOs with our proposed work. A comprehensive overview is also presented here.

The present study is aimed at designing bilayer-floating tablets to improve the drug concentration in the stomach for enhanced therapeutic efficacy. The tablets are comprised of an upper layer of levofloxacin (466.5 mg) and a lower layer of famotidine (133.5 mg). Five formulations (F1-F5) were developed by using hydroxypropyl methylcellulose grades (K4M, K15M, and K100M) along with Carbopol 934. In the case of the effervescent system (F1-F3), sodium bicarbonate was added to impart buoyancy to the tablets; while in the case of noneffervescent formulations (F4 & F5), guar gum and xanthan gum were incorporated to induce flotation and swelling and retard the release of a drug. The precompression characteristics of tablets depict the suitability of all formulation powder for direct compression. The ATR-FTIR analyses have shown that the components of both effervescent and noneffervescent tablets are compatible with each other. The total weight of each tablet was 600 mg, with a weight variation of about ≤10 mg. Both the layers were smooth and flat with a thickness ranging from 3.16±0.04 to 3.54±0.01 mm. The diameters of prepared floating tablets were about 15 mm, optimum for oral administration. After adjusting the tablet’s hardness to 6-7 kg/cm2, its friability was found to be

In recent decades, because of the speedy progress of the smart grid and the deepening of the reforms of the energy system, demand-side users can contribute to the collaboration of the energy network, with the main right to public energy procurement and the main right to sell energy. The demand side of the smart grid and the open energy market provides users with more adoptions, and game theory is expected to become an important tool for optimizing multi-stakeholder decision-making and solving many problems in this area. In this regard, this review article first reviews the recent development of game theory application in modern power systems, in addition to discussing in detail the typical gaming behavior of the current energy demand side. Second, it focuses on the application of game theory mainly in three aspects: distributed energy users, high-energy energy users, and medium- and low-energy users. Game theory is used in optimizing the distributed energy coordination, optimizing the energy purchasing strategy, responding to the needs of commercial and residential users, and ensuring network communication. Later, a comprehensive analysis of recent trends in game theory application in power systems is carried out in detail.

Advancement in mobile phone (MP) technology has revolutionized the lifestyle. In recent years, we observed that MP technology had been involved in almost all aspects of life, such as communication purposes, e-commerce, mobile baking, and social media connectivity. So, it becomes a hot research topic to select the best MP that fulfills the desired feathers requirement. In this paper, the expert’s familiarity with the examined objects is factored into the initial judgments under the T-spherical fuzzy sets (T-SFSs) environment. The T-SFS is the extension of the picture fuzzy (PF) set (PFS), which gives wider scope for finding the most precise options than existing fuzzy frameworks. The multiattribute decision-making (MADM) is a common and valuable method for aggregating information. For MADM, various aggregation operators (AOs) have been created over the years. The article introduces the newly proposed approach T-spherical fuzzy (T-SF) confidence level weighted averaging T−SFWAc and T-SF confidence level weighted geometric T−SFWGc. Also, some desired properties of AOs are discussed, and the T-SF entropy measure is introduced for selecting the weight criteria. A MADM framework is introduced, on the behalf of proposed operators. The proposed MADM framework is applied to solve the real-life example of consumers’ preferences to show effectiveness and practicality. Lastly, the developed framework is set side by side with other prevailing approaches to demonstrate the superiority and significance of other existing AOs.

Solar power is an alternative energy derived from the sun. Solar power is more environmentally friendly and sustainable than burning fossil fuels which releases harmful greenhouse gas emissions. Therefore, this study aims to evaluate a reliable solar panel based on certain characteristics by incorporating the theory of the decision-making process. To serve this goal, this study discusses a well-known aggregation model of the q-rung orthopair fuzzy set, which is a broader and flexible environment of fuzzy sets and intuitionistic fuzzy sets used to handle unpredictable information of human opinions. The key components of this article are to demonstrate some realistic operations of Sugeno–Weber triangular norms considering q-rung orthopair fuzzy information. These operations provide authentic estimated information during the decision-making process. We developed a class of new aggregation operators using the q-rung orthopair fuzzy information system, including q-rung orthopair fuzzy Sugeno–Weber power weighted average and q-rung orthopair fuzzy Sugeno–Weber power weighted geometric operators. Some realistic characteristics and special cases are also demonstrated to show the compatibility of the proposed methodologies. An innovative approach to the multi-attribute decision-making problem is utilized to resolve different real-life applications considering various criteria or attributes. To show the intensity and applicability of the proposed approaches, we explored a numerical example for efficient solar panel selection based on the proposed methodologies. Furthermore, we presented a comprehensive comparison technique to compare the findings of the existing methods with the proposed aggregation approaches. Finally, the proposed research work is summarized, and the future prospects are discussed.

Abstract Aggregation operators (AOs) are utilized to overcome the effects of attributes under some specific degree of weight in the decision-making (DM) process. The AOs have a large capacity to deal with uncertain and unpredictable information in multi-attribute decision-making (MADM) problems. The Hamy mean (HM) aggregation tools are well-known aggregation models, which are utilized to define correlation among different input arguments adequately. The intuitionistic fuzzy (IF) sets (IFS) can express unpredictable and vague information. The Aczel Alsina aggregation expressions are extensions of triangular norms. Recently, Aczel Alsina aggregation tools attained a lot of attentions from numerous research scholars. By inspiring the robustness and reliability of Aczel Alsina aggregation tools, we expose some appropriate operations of Aczel Alsina expressions under consideration of IF information. In this manuscript, we developed an intuitionistic fuzzy Aczel Alsina HM (IFAAHM) and an intuitionistic fuzzy Aczel Alsina weighted HM (IFAAWHM) operator. We also expressed the theory of Dual HM (DHM) tools and established a series of new approaches including intuitionistic fuzzy Aczel Alsina Dual HM (IFAADHM) and intuitionistic fuzzy Aczel Alsina weighted Dual HM (IFAAWDHM) operators. Some reliable characteristics and special cases of our derived approaches are also presented. The authors solved an application of a MADM technique under consideration of our derived approaches. To check the reliability and dependency of our derived mythologies, we gave an experimental case study to evaluate a desirable construction material based on some specific criteria of different Alternatives. To see the advantages and compatibility of our derived approaches, by comparing the results of existing approaches with the results of currently discussed AOs.

The Aczel-Alsina t-norm and t-conorm were derived by Aczel and Alsina in 1982. They are modified forms of the algebraic t-norm and t-conorm. Furthermore, the theory of picture fuzzy values is a very valuable and appropriate technique for describing awkward and unreliable information in a real-life scenario. In this research, we analyze the theory of averaging and geometric aggregation operators (AOs) in the presence of the Aczel-Alsina operational laws and prioritization degree based on picture fuzzy (PF) information, such as the prioritized PF Aczel-Alsina average operator and prioritized PF Aczel-Alsina geometric operator. Moreover, we examine properties such as idempotency, monotonicity and boundedness for the derived operators and also evaluated some important results. Furthermore, we use the derived operators to create a system for controlling the multi-attribute decision-making problem using PF information. To show the approach's effectiveness and the developed operators' validity, a numerical example is given. Also, a comparative analysis is presented.

Multi-attribute group decision-making (MAGDM) is an interesting technique to find the most optimal alternative among comparative alternatives. Several authors put forward to MAGDM by introducing different fuzzy frameworks and also different tools to deal with fuzzy information. Intuitionistic fuzzy set (IFS) is the fuzzy framework that deals with the uncertainty in MAGDM. Due to their flexibility and generality, Frank t-norm (FTNM) and t-conorm (FTCNM) play an essential role in information fusion. Moreover, as the generalization of some mean operators, the Maclaurin symmetric mean (MSM) operator considers the relationship between multi-criteria arguments, especially in MAGDM. This article aims to develop some MSM aggregation operators (AOs) for the intuitionistic fuzzy set (IFS) based on FTNM and FTCNM and to apply newly developed AOs in the MAGDM. To utilize the MAGDM algorithm, first, we defined the MSM by using the FTNM and FTCNM in the environment of IFS. Then we proposed intuitionistic fuzzy (IF) Frank MSM (IFFMSM) and IF Frank weighted MSM (IFFWMSM) operators. Then, the fundamental properties of these AOs are stated and proved. Then, the strategy is given that accounts for the application of the newly developed family of AOs. Further, freshly defined operators are applied to the MAGDM problem with the help of an example where the risk factors of the construction industry are assessed. To cope with the significance, the proposed AOs are compared with some existing AOs. This study also addresses the variation of these AOs' behavior based on the interpretation of sensitive parameters.

The goal of this manuscript is to introduce the JK iterative scheme for the numerical reckoning of fixed points in generalized contraction mappings. Also, weak and strong convergence results are investigated under this scheme in the setting of Banach spaces. Moreover, two numerical examples are given to illustrate that the JK iterative scheme is more effective than some other iterative schemes in the literature. Ultimately, as an application, the JK iterative scheme is applied to solve a discrete composite functional differential equation of the Volterra-Stieljes type.

Solubility is an essential criterion for attaining desired concentration of the drug within the systemic circulation to ensure intended pharmacological action. The main setback for the formulation development of new chemical entities and generic drugs is their lower aqueous solubility. Therefore, a drug carrier system is needed which not only enhances the solubility of low aqueous soluble drugs but also maintains a constant pharmacological action of drugs within predetermined intervals of time. For this purpose, authors prepared carbopol 934-co-poly(itaconic acid) (CPcPIA) nanogels by the free radical polymerization technique for the solubility enhancement of Valsartan. The polymeric nanogels were characterized and studied for further evaluation. FTIR studies indicated no interactions between the drug and nanogel contents. SEM showed a porous and sponged structure of particles without any agglomeration. Similarly, higher thermal stability was detected for the fabricated nanogel compared to its constituents, while reduction in crystallinity of the drug and excipients was shown by XRD analysis, indicating the amorphous nature of the polymeric nanogels. Average particle size and zeta potential of prepared nanogels were found 290.32 nm and –8.32 mV, respectively. Furthermore, various studies such as sol-gel fraction, dynamic swelling, drug loading, in-vitro drug release studies, solubility, and toxicity study were conducted for the developed nanogels. A significant increase in the solubility of Valsartan (2.002, 2.976, and 3.543 mg/mL) was observed by polymeric nanogels in pH 1.2, deionized distilled water, and pH 7.4 as compared to reference product. Toxicity study indicated no toxic effect of prepared nanogels on rabbit's species. Thus, it can be demonstrated from the results that synthesized nanogels are not only limited to a specific class of drug but the solubility of all low aqueous soluble drugs can be enhanced by the prepared networks of nanogels.

The fusion of information is a very hectic process whenever we analyze the information. Several frameworks have been introduced to reduce the uncertainty while fusing the information. Among those techniques, the Pythagorean fuzzy rough set (PyFRS), which is based on approximations is a key idea for dealing with uncertainty when data is taken from real-world circumstances. Furthermore, the most adaptable and flexible operational laws based on the parameters for fuzzy frameworks are Aczel-Alsina t-norm (AATNM) and Aczel-Alsina t-conorm (AATCNM). The major goal of this work is to introduce some methods for the basic operations of the information in the shape of Pythagorean fuzzy rough (PyFR) values (PyFRVs). Consequently, the PyFR Aczel-Alsina weighted geometric (PyFRAAWG), PyFR Aczel-Alsina ordered weighted geometric (PyFRAAOWG), and PyFR Aczel-Alsina hybrid weighted geometric (PyFRAAHWG) operators are developed in this article based on AATNM and AATCNM. Further, some basic properties of the developed operators are observed and discussed. Further, the developed approaches are applied to the problem of multi-attribute group decision-making (MAGDM). The obtained results from the MAGDM problem are observed at various values of the parameters involved by AATNM and AATCNM. Moreover, the results are also compared with already existing techniques for the significance of the developed approach.

The ability of the Maximum Power Point Tracking (MPPT) technology to prevent losses by stabilizing power fluctuations during severe weather conditions is critical in improving photovoltaic power generation systems. Overall system stability is improved by carefully tracing the maximum power point (MPP). This research focuses on improving MPPT performance in solar systems by employing the ''Fuzzy Logic'' control method. The simulation, which is run in MATLAB/Simulink, includes a detailed model of the entire system. The primary circuit is designed with a DC-DC Boost architecture and a single MOSFET transistor. The Fuzzy Logic Controller (FLC) unit in MATLAB/Simulink generates an output variable led by two input variables via the Fuzzy Logic Controller unit. The Fuzzy Logic Controller (FLC) unit generates an output variable led by two input variables in MATLAB/Simulink. The simulation model, called ''Fuzzy Disturbance,'' combines Perturb & Observe with Fuzzy Logic and runs for 3 s. The results show an essential increase in system efficiency to 97%. The simulation results show that the suggested approach tracks MPP, reduces output power fluctuations, and improves system efficiency.

This manuscript is devoted to presenting some convergence results of a three-step iterative scheme under the Chatterjea–Suzuki–C ((CSC), for short) condition in the setting of a Banach space. Also, an example of mappings satisfying the (CSC) condition with a unique fixed point is provided. This example proves that the proposed scheme converges to a fixed point of a weak contraction faster than some known and leading schemes. Finally, our main results will be applied to find a solution to functional and fractional differential equations (FDEs) as an application.

The goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called (α,β,γ)-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the K-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the K-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the K-type iterative method to solve a variational inequality problem on a Hilbert space.

This paper introduces some numerical algorithms for finding solutions of nonlinear problems like functional equations, split feasibility problems (SFPs) and variational inequality problems (VIPs) in the setting of Hilbert and Banach spaces. Our approach is based on the Thakur-Thakur-Postolache (TTP) iterative algorithm and the class of mean nonexpansive mappings. First we provide some convergence results (including weak and strong convergence) in the setting of Banach space. To support these results, we provide a numerical example and prove that our TTP algorithm in this case converges faster to fixed point compared to other iterative algorithms of the literature. After that, we consider two new TTP type projection iterative algorithms to solve SFPs and VIPs on the Hilbert space setting. Our result are new in analysis and suggest new type effective numerical algorithms for finding approximate solutions of some nonlinear problems.

The cryptocurrency, often known as virtual or digital currency, is one of the most significant breakthroughs brought about by digitalization. It has been mentioned recently, an innovative system for stockholders in particular. Cryptocurrencies of all kinds, including Bitcoin, Shib, Dogecoin, and Tether are decentralized. Categorization complicates decision-making (DM) as well as the transfer of uncertainty and digital currency validation. The multi-attribute group decision-making (MAGDM) method is defined in this article using the Frank weighted averaging and Frank weighted geometric aggregation operators (AOs). This research examines the uniqueness of the qRung orthopair fuzzy hypersoft set (qROFHSS) that is responsive to volatilities, vagueness, doubt, and inaccurate data. Additionally, some specific essential qROFHSS operational laws are defined in this study. The framework presented here is the best alternative for understanding electronic money. This research supports the difficulty of situations involving making choices that must take into account a variety of qualities and sub-attributes to select the best choice. We see that Bitcoin has a variety of applications and that cryptocurrencies have an excellent chance to emerge as a prominent benefit lesson in financial choice-making. In this paper, to demonstrate the viability of the suggested methodology we look at a case study on choosing the best currency out of these that are accessible to manage cryptocurrency. Comparative analysis shows that the suggested strategy is stable and good. We conclude that the proposed methodology provides a thorough and systematic approach to analyzing cryptocurrency. Finally, a numerical example is provided to show the method’s efficiency.

We introduce the concept of spherical fuzzy neutral aggregation operators by utilizing neutral addition and scalar multiplication operational laws. Spherical fuzzy set (SFS) is an effective tool for handling cognitive uncertainty in decision-making (DMg), and neutral operations are particularly useful for capturing the biased preferences of decision-makers (DMs). In this context, the primary aim of this study is to innovate novel operational laws and their associated aggregation operators. Therefore, the main contribution of this manuscript is the development of several neutral aggregation operators (NAOs) based on SFS, including the spherical fuzzy weighted neutral aggregation (SFWNA) operator, the spherical fuzzy ordered weighted neutral aggregation (SFOWNA) operator, and the spherical fuzzy hybrid neutral aggregation (SFHNA) operator. These NAOs are specifically designed for the multi-attribute group decision-making (MAGDM) algorithm. In order to showcase the efficacy of the proposed algorithm, we implemented it in the context of selecting a suitable site for an olive tree plantation in the Punjab province of Pakistan. The algorithm successfully evaluated various plantation locations (alternatives) based on the considered criteria. The results illustrate the flexibility, consideration of the interaction of coefficients, desirable characteristics, applicability to MAGDM, and effectiveness of the proposed AOs and DMg scheme. These outcomes provide valuable insights into the advantages and potential impact of this novel approach in addressing real-world problems within a fuzzy environment. Finally, the obtained results were compared with several existing techniques, confirming that the suggested method produces valid and reliable outcomes.

The complex q-Rung orthopair fuzzy (Cq-ROF) sets are an extended version of the fuzzy sets and q-rung orthopair fuzzy circumstances. The Cq-ROF set carried extensive information about an object with two components: membership grade (MG) and non-membership grade (NMG). The MG and NMG enlarged the unit circle to a complex plane. The decision maker evaluates complex and complicated information more accurately considering the Cq-ROF domain. This article aims to present the importance of energy sources, and we discuss the application for the selection of a suitable company selection for dam construction. Dams are the most appropriate and cheap sources to produce electricity. Now, the day’s importance of electricity is not ignorable. So, construct the multi-attribute group decision-making (MAGDM) methodology by utilizing Aczel-Alsina (AA) t-norm (TN) and t-conorm (TCN) operational laws with power aggregation operators (PAO) to solve the appropriate company selection problem for dam construction. PAO provides more accurate aggregation results between the several attributes. Finally, we define the Cq-ROF Aczel-Alsina power-weighted averaging (Cq-ROFAAPWA) and aggregation Cq-ROF Aczel-Alsina power-weighted geometric (Cq-ROFAAPWG) operators. Also, some fundamental axioms are discussed. By applying the proposed Cq-ROFAAPWA and Cq-ROFAAPWG operators, solve the real-life MAGDM problematic issue through a numerical example. For the superiority and applicability of proposed techniques, provide a comprehensive comparative analysis with other prevailing aggregation operators (AOs). In the end, provide solid conclusions.

The power Bonferroni mean (PBM) is a combined networking system that can benefit both the power average (PA) operator, which might attenuate the effects of irrational data provided by the prejudiced decision-makers (DMs), and the BM operator, which may incorporate the interconnections between any two attributes. In this paper, we defined the aggregation operators (AOs), such as the power average (PA) operator and the power Bonferroni mean (PBM) operator, based on the Aczel-Alsina (AA) operational rules under the environment of the q-Rung Orthopair fuzzy set (q-ROFS), and provided their specific characteristics for the solution of numerical problems. We extend the power Bonferroni mean (PBM) operator under the framework of q-ROFVs to establish the q-Rung Orthopair Fuzzy Aczel-Alsina power Bonferroni mean (q-ROFAAPBM) operator and the q-Rung Orthopair Fuzzy Aczel-Alsina weighted power Bonferroni mean (q-ROFAAWPBM) operator and discuss a few of the most useful properties of these AOs. After that, the q-ROFAAWPBM operator is used to solve the multi-attribute decision-making steps for q-ROFVs. The disease is diagnosed with the MADM method, which shows its usefulness and effectiveness. Finally, the comparison of our developed approach has been demonstrated to be superior and more effective than the existing literature, and we can conclude the result.

Complex T-spherical fuzzy set (CTSF) is the extended form of complex spherical fuzzy set (CSFs). CTSF can extract the maximum information from real-life phenomena with the help of a membership degree (MD), abstinence degree (AD), and non-membership degree (NMD). Due to this nature, CTSF can describe every human opinion’s phenomenon with less uncertainty. The major contribution of this article is to develop an interesting approach to aggregate the information in the form of the CTSFS. To do this, first, we develop the operational laws for CTSF values (CTSFVs) based on Frank’s operational laws. Then two types of aggregation operators (AOs), CTSF Frank weighted averaging (CTSFWA) and CTSF Frank weighted geometric (CTSFFWG) operators are introduced based on the Frank t-norm (FTNM). Further, some basic properties of the CTSFFWA and CTSFFWG operators are studied. The developed approach is also applied to the real-life problem of multi-attribute decision-making (MADM) where the soil fertility is assessed based on some factors affecting the soil fertility. The sensitivity of the developed approach is observed with the variation of the involved parameter graphically. The comparison of the developed approach is also studied and as well as graphed.

To reduce the risk and interruptions of the supply chain, some appropriate aggregation operators are used to deal with crucial challenges and to keep the support system reliable. In this article, we explore the notion of the complex picture fuzzy (CPF) set (CPFS), a wider framework of fuzzy and picture fuzzy sets. Some robust operations of the Aczel Alsina aggregation tools are characterized based on CPF information to overcome the impact of uncertain and imprecision situations. We also explain an innovative concept of the prioritized aggregation operators (AOs) in the light of CPF information. The theory of unknown weight vectors is used to develop some new approaches of the CPF environments, including CPF Aczel Alsina prioritized average (CPFAPA) and CPF Aczel Alsina priortized geometric (CPFAPG) operators. We also propose a class of new methodologies under considering CPF information, such as CPF Aczel Alsina prioritized weighted average (CPFAPWA) and CPF Aczel Alsina prioritized weighted geometric (CPFAPWG) operators. To illustrate the flexibility of our invented methodologies, some appropriate characteristics of the proposed approaches are also demonstrated. The multi-attribute decision-making (MADM) technique is used to evaluate many crucial real-life challenges. An algorithm for the MADM problem is also proposed to show the robustness of our invented approaches. By using proposed methodologies, we demonstrate an experimental case study to choose a sustainable supplier agnet based on CPF information. To show the practicability and consistency of our invented approaches by contrasting the results of existing approaches in the literature review with currently presented methodologies.

In this article, we expose the notion of power operator to reduce the impact of negative information on the decision-making (DM) process. The power aggregation tools are also robust mathematical aggregation operators (AOs) which allow input arguments to support each other in the DM process. The Frank aggregation expressions are reliable and updated versions of triangular norms which are used to handle complex and complicated information in a decision-making process. The picture fuzzy (PF) set (PFS) is an extended version of the fuzzy sets (FSs) and intuitionistic FSs (IFSs). A PFS has four terms of an object simultaneously such as positive grade (PG), Abstained grade (AG), negative grade (NG) and refusal grade (RG). By using basic operations of Frank aggregation expressions, we propose a list of new appropriate methodologies under consideration of PF information, including “picture fuzzy frank power average” (PFFPA), and “picture fuzzy frank power geometric” (PFFPG) operators. We also present some new approaches to PFSs based on Frank aggregation tools such as “picture fuzzy frank power weighted average” (PFFPWA) and “picture fuzzy frank power weighted geometric” (PFFPWG) operators. Some appropriate properties and special cases of our currently proposed approaches are also studied. Moreover, to ratify the intensity and reliability of our derived strategies, we illustrated an algorithm of the multi-attribute group decision-making (MAGDM) technique under a PF environment. Furthermore, we illustrated a practical case study to evaluate a suitable optimal option by considering our proposed approaches and analyzed the performance of our currently derived approaches by comparing the results of existing methodologies.

Multi-attribute decision-making (MADM) technique has been widely utilized in many domains, including management, economics, and other disciplines. It plays a significant role in the mainstream of decision science. Its main process is to rearrange available choices and select the optimal option out of a group of options based on certain characteristics assigned by the decision maker. Aggregation operators (AOs) play a significant role in MADM techniques to aggregate uncertain and vague information. Aczel Alsina aggregation models are recently introduced to handle ambiguous and dubious information, Aczel Alsina aggregation models attained a lot of attention from numerous research scholars. This article aims is to generalize the concept of pythagorean fuzzy sets (PyFSs) in the framework of interval-valued pythagorean fuzzy (IVPyF) sets (IVPyFSs) by utilizing the basic operations of Aczel-Alsina aggregation models. We developed a list of certain AOs of IVPyFSs based on Aczel-Alsina aggregation models namely “IVPyF Aczel-Alsina weighted averaging” (IVPyFAAWA), “IVPyF Aczel-Alsina ordered weighted averaging” (IVPyFAAOWA), and “IVPyF Aczel-Alsina hybrid weighted averaging” (IVPyFAAHWA) operators. We also studied some appropriate AOs of IVPyF information such as the “IVPyF Aczel-Alsina weighted geometric” (IVPyFAAWG) operator. We also interpreted certain characteristics of our invented approaches. To check the effectiveness and reliability of our proposed approaches, we established an illustrative numerical example for the selection of a research scientist under the system of the MADM technique. We also explored sensitivity analysis, in which we evaluated the impact of parametric values on the result of our proposed approaches. Furthermore, we also illustrated a realistic comparison in which we compare the outcomes of exiting methodologies with the results of our invented approaches.

Green intelligent building materials is an effective way for building materials industry to reduce carbon. However, a small amount of research and development (R&D, unstable R&D investment and imperfect collaborative innovation mode hinder the development of green intelligent building materials industry. However, few scholars study the development mechanism of green intelligent building materials industry from the perspective of industrial chain considering the above obstacles. In this study, the game models under market mechanism and government regulation were constructed to analyze the income distribution mechanism for the development mechanism of green intelligent building materials industry. Finally, the questionnaire method was used to discuss the game strategy of collaborative innovation behavior among agents. The results are as follows. In the game strategy selection of collaborative innovation behavior among green intelligent building materials, factors such as database marketing maturity, information flow and technology volume generated by collaborative innovation, technical benefit coefficient, social benefit coefficient and profit and loss barrier factors are conducive to the collaborative innovation behavior of green intelligent building materials. When the market mechanism fails, the incentive effect of cost subsidy adopted by the government is more efficient and fast, and the driving force of achievement reward is more lasting. The combination of the two incentives is the best. Moderate supervision and punishment lower than the free rider income can not ensure fair competition among green intelligent building materials enterprises. The punishment above the threshold can effectively restrain the negative impact of free rider income and prospect profit and loss. This study not only theoretically expands the development theory of digital industry from the perspective of industrial chain by considering the maturity factor of database, but also provides policy guidance for the development of green intelligent building materials industry in practice.

Due to the rapid development of the economy, science, and technology, we have noticed a trend where less and less attention is being paid to the modernization and development of labor and reading concerning agricultural teaching methods. Using the entropy weight method and the analytic hierarchy process, this paper empirically evaluates the practical aspects of interdisciplinary farming at agricultural colleges. In addition, it analyzes problems with current practical teaching methods from the perspectives of curriculum materials, practical education, educational platforms, and teachers. We also put forward corresponding ideas and suggestions for practical teaching methods related to interdisciplinary farming. The results show the following: ⅰ) A student's sense of responsibility to develop agriculture should be cultivated by integrating the cultural elements of agriculture with science curricula. ⅱ) Faculties with knowledge of interdisciplinary practices should be set up to improve students' abilities regarding practical activities. ⅲ) A practical teaching platform should be established to provide conditions for interdisciplinary integration. ⅳ) The previous conclusion requires schools to cultivate high-level teachers to maximize their leading role; only in this way can the process of agricultural education be comprehensively promoted. In this paper, by studying practical farming teaching methods at agricultural colleges and universities, we found that farming culture can be enhanced by educational culture. The cultivation of agricultural talents in the new era can be aided by helping students understand and appreciate agriculture, and by disseminating farming culture, agricultural talent can be cultivated among these students. Furthermore, this study focuses on cultivating excellent talent in terms of technical agriculture and rural management, thus combining theory and practice, which will promote the spirit of labor among students, as well as professional quality. This will ensure the constant innovation of agricultural and nonagricultural professional services for agriculture, rural areas, and farmers.