Neutrosophic Set Research Articles

An adaptive feature mode decomposition based on a novel health indicator for bearing fault diagnosis

In this paper, a novel scheme for detecting bearing defects is proposed utilizing single-valued neutrosophic cross-entropy (SVNCE). Initially, the artificial hummingbird algorithm (AHA) is used to make the feature mode decomposition (FMD) adaptive by optimizing its parameter based on a novel health indicator (HI) i.e. sparsity impact measure index (SIMI). This HI ensures full sparsity and impact properties simultaneously. The raw signals are decomposed into different modes by adaptive FMD at optimal values of its parameters. The energy of these modes is calculated for different health conditions. The energy interval range has been decided based on energy eigen which are then transformed into single-valued neutrosophic sets (SVNSs) for unknown defect conditions. The minimum argument principle employs the least SVNCE values between SVNSs of testing samples and SVNSs of training samples to recognize the different defects in the bearing. The proposed methodology is applied to bearing from industrial mechanical systems.

Single Valued Neutrosophic Set with Multi-Criteria Decision Making Methodology for Wind Turbine Development

Taller hubs and longer blades make wind turbines more practical and economical than their predecessors because they lower the energy production cost per unit. Nonetheless, these buildings stand out more in the environment because of their larger scale. As wind turbine exposure increases, communities become more concerned about the environment and economy. Thus, a conflict arises between the benefits of increased visibility and reduced wind energy prices as wind turbines become bigger. Most MCDM applications emphasize the significance of wind turbine visibility, which they define as the separation from populated areas, coastal regions, etc. The increased distance from a possible turbine location lessens the influence of visibility, or vice versa. This supposition contributes to the MCDM's visible effects in part. On the other hand, determining visibility may provide more accurate and practical geographic data to be used as a determining factor. This study used an MCDM methodology to show the relationships between wind turbine criteria. The DEMATEL method is an MCDM method used to show wind turbine weights. The DEMATEL method shows the relationships between criteria. There are 12 criteria used in this study. The DEMATEL method was integrated with the single-valued neutrosophic set (SVNS) to overcome uncertainty in the evaluation process.

Enhanced group decision-making through an intelligent algorithmic approach for multiple-attribute credit evaluation with 2-tuple linguistic neutrosophic sets

With the development of the internet economy, e-commerce has rapidly risen, and a large number of small and micro e-commerce enterprises have emerged. However, these enterprises have low financial information transparency, small scale, and high development uncertainty. Therefore, combining the characteristics of the internet economy, it is of great significance to dynamically evaluate credit risk. This not only helps to enhance the quality and rationality of credit risk evaluation results, but also helps to improve financing efficiency and reduce financing risks. The credit evaluation for small and micro enterprises is a multiple-attribute group decision-making (MAGDM). Recently, the TODIM (an acronym in Portuguese of interactive and multicriteria decision making) and TOPSIS method has been inaugurated to cope with MAGDM issues. The 2-tuple linguistic neutrosophic sets (2TLNSs) are inaugurated as an effective tool for characterizing uncertain information during the credit evaluation for small and micro enterprises. In this paper, the 2-tuple linguistic neutrosophic TODIM-TOPSIS (2TLNN-TODIM-TOPSIS) method is inaugurated to solve the MAGDM under 2TLNSs. Finally, a numerical case study for credit evaluation for small and micro enterprises is inaugurated to confirm the proposed method. The prime contribution of this paper are outlined: (1) The information entropy based on score function and accuracy function are built on the 2TLNSs to obtain weight information; (2) an integrated the 2-tuple linguistic neutrosophic TODIM-TOPSIS (2TLNN-TODIM-TOPSIS) method is established to cope with MAGDM; (3) An illustrative example for credit evaluation for small and micro enterprises has accomplished to illustrate the 2TLNN-TODIM-TOPSIS; (4) some comparative analysis are employed to verify the 2TLNN-TODIM-TOPSIS method.

Investigation of a neutrosophic group

We use a neutrosophic set, instead of an intuitionistic fuzzy because the neutrosophic set is more general, and it allows for independent and partial independent components μ (χ) , γ (χ) , ζ (χ), while in an intuitionistic fuzzy set, all components are totally dependent. In this article, we present and demonstrate the concept of neutrosophic invariant subgroups. We delve into the exploration of this notion to establish and study the neutrosophic quotient group. Further, we give the concept of a neutrosophic normal subgroup as a novel concept.

Modified MABAC for MCGDM with interval-valued neutrosophic sets and application to design quality evaluation of digital cultural and creative products

With the development of digital creative industry and the use of more emerging digital technologies, the forms of digital cultural and creative design products are also increasingly diversified. Unlike traditional cultural and creative design products, digital cultural and creative design products are no longer limited to physical products, but appear more in the field of exhibition, virtual reality and product visualization. At the initial stage of the combination of digital information technology and cultural and creative content, digital cultural and creative design products, unlike ordinary cultural and creative design products, opened a new vision for users. The design quality evaluation of digital cultural and creative design products is viewed as a multi-criteria group decision-making (MCGDM). The single-value neutrosophic sets (SVNSs) concept and its interval-valued version (Interval-valued neutrosophic sets, IVNSs) are within the recent rapid developments for managing the uncertain representation problem in MCGDM. In SVNSs, decision makers (DMs) could portray membership, non-membership and hesitancy. IVNSs expands this useful feature through portraying intervals to these three information decision degrees. In this manner, the uncertainty, ambiguity and vagueness hidden in human judgements could be quantified more efficiently. IVNSs have been widely employed and researched in MCGDM. The main purpose of this paper is to proposed the Interval-valued neutrosophic number MABAC (IVNN-MABAC) technique based on prospect theory (PT) to address the MCGDM. Eventually, an example for design quality evaluation of digital cultural and creative design products and some comparative analysis was employed to demonstrate the superiority of the designed technique.

Smart algorithmic solutions for audience service quality evaluation for large-scale sports-events through harnessing interval neutrosophic EDAS and CRITIC Technique

Sports events, as large-scale events that provide products and services, have received widespread attention for their economic benefits and influence. Event organizers expect to achieve high efficiency by providing high-quality products and services. The quality of competition products and services is mainly evaluated through the subjective feelings of the audience, and usually the audience’s evaluation of service quality is vague. Therefore, this article intends to establish an evaluation index system for the quality of spectator service in sports events, in order to provide a reasonable evaluation of the service products provided by sports event organizers. The audience service quality evaluation for large-scale sports-events is a MAGDM problems. Recently, the EDAS and CRITIC technique has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for characterizing uncertain information during the audience service quality evaluation for large-scale sports-events. In this paper, the interval neutrosophic number EDAS (INN-EDAS) technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs. The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs. Finally, a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique. The main contributions of this paper are proposed: (1) The INN-EDAS technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs; (2) The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs; (3) a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique.

Enhanced EDAS technique for colleges business English teaching quality evaluation based on Euclid distance and cosine similarity measure

With the development of national economy and the increase of foreign trade, Business English has become one of the most popular majors in universities. In order to cultivate business English talents for the national society and adapt to the requirements of the times, the innovation of English teaching concepts and the reform of teaching techniques are the only way for business English majors teaching in universities. The colleges business English teaching quality evaluation is considered as a multi-attribute group decision making (MAGDM). In this paper, the EDAS technique is expanded to the single-valued neutrosophic sets (SVNSs) and the single-valued neutrosophic number EDAS (SVNN-EDAS) technique based on Euclid distance and cosine similarity measure (CSM) is constructed to manage MAGDM. The CRITIC technique is employed to achieve the weight information based on Euclid distance and CSM technique under SVNSs. Finally, the colleges business English teaching quality evaluation is employed to demonstrate the SVNN-EDAS technique and some comparative analysis is employed to demonstrate the SVNN-EDAS. Thus, the main research contribution of this work is then constructed: (1) the CRITIC technique is built to get the attribute’s weight based on Euclid distance and CSM technique; (2) the SVNN-EDAS technique is constructed under SVNNs based on Euclid distance and CSM technique; (3) an example for colleges business English teaching quality evaluation is employed to verify SVNN-EDAS technique and several decision comparative analysis are employed to verify the SVNN-EDAS.

Method for multiple attribute decision making with single-valued neutrosophic information and application to development level evaluation of rural preschool education

The development of rural preschool education (RPE) is not only related to the healthy growth of rural preschool children, but also to social fairness and sustainable development. Therefore, the development of RPE not only involves the expansion of quantity, but also the improvement of its quality. At present, in China’s RPE, the determination of value goals There are still many obstacles in terms of source supply, institutional mechanism construction, development mode selection, and external environment construction, which make the high-quality development of RPE lack good internal motivation and external support. In view of this situation, some researchers have begun to explore the high-quality and sustainable development of RPE differently. However, the high-quality development of RPE is a systematic reform project that needs to start from the present. From multiple perspectives such as reality and history, internal and external education, this paper examines the systematic and global nature of RPE reform and development. The development level evaluation of RPE is a MADM. In this paper, the generalized weighted Bonferroni mean (GWBM) decision operator and power average (PA) is designed to manage the MADM under single-valued neutrosophic sets (SVNSs). Then, the generalized single-valued neutrosophic number power WBM (GSVNNPWBM) decision operator is constructed and the MADM model are constructed based on GSVNNPWBM decision operator. Finally, a decision example for development level evaluation of RPE and some useful comparative studies were constructed to verify the GSVNNPWBM decision operator.

A flexible group decision-making method for informationization teaching ability evaluation of university teachers integrating ExpTODIM and GRA under interval neutrosophic environment

Today, information technology has penetrated into various fields of universities, and the development of information technology in teaching, scientific research, management, and services has become a catalyst for promoting changes in universities. In terms of teaching informatization, the Internet provides a powerful tool for knowledge dissemination and a huge platform for learning and communication between university teachers and students. Knowledge sharing has become easier, and the era of mutual interaction between teachers and students has arrived. University teachers need to quickly face this challenge, adapt to the new teaching and learning environment, improve their own literacy, enhance their information-based teaching ability, change their teaching behavior, and thereby improve the quality of university education and meet the needs of society for talent cultivation. The informationization teaching ability evaluation of university teachers is a classical MAGDM problems. Recently, the Exponential TODIM(ExpTODIM) and (grey relational analysis) GRA method has been used to cope with MAGDM issues. The interval neutrosophic sets (INSs) are used as a tool for characterizing uncertain information during the informationization teaching ability evaluation of university teachers. In this manuscript, the interval neutrosophic number Exponential TODIM-GRA (INN-ExpTODIM-GRA) method is built to solve the MAGDM under INSs. In the end, a numerical case study for informationization teaching ability evaluation of university teachers is given to validate the proposed method.

Lagrange-enhanced GRA framework for probabilistic simplified neutrosophic multiple-attributes decision-making and applications to painting teaching quality evaluation

Universities are important talent training bases in China and the main driving force for achieving the strategic layout of “revitalizing the country through science and education” and “strengthening the country through talent". Oil painting is a global art with rich humanistic and artistic value. Most art colleges in China have set up oil painting courses. Analyze the current situation and value of oil painting course teaching in local art (teacher training) majors, and leverage the educational role of oil painting courses by enriching course offerings, emphasizing the integration of humanistic innovation, improving teacher literacy, and striving to further improve the quality and efficiency of oil painting course teaching. The quality evaluation of oil painting teaching in universities is viewed as multiple-attribute decision-making (MADM). The grey relational analysis (GRA) is a useful tool to cope with the MADM issue. The probabilistic simplified Neutrosophic set (PSNSs) is easy to characterize uncertain information during the quality evaluation of oil painting teaching in universities. In this paper, in order to obtain the weight information, an optimization model implemented to obtain a simple and exact formula which can be employed to derive the attribute weights values based on the Lagrange function and the probabilistic simplified neutrosophic number grey relational analysis (PSNN-GRA) technique is implemented for MADM to rank the alternatives. Finally, a numerical example for quality evaluation of oil painting teaching in universities is used to verify the practicability of the PSNN-GRA technique and compares it with other techniques.

Cross-entropy method for interval-valued neutrosophic number multiple attribute decision making for education quality management evaluation in higher education institutions

Under the premise of today’s socialist modernization construction, the development and progress of the country require more outstanding talents such as aspiring youth and intellectuals to participate, which puts forward higher requirements for education quality indicators and various aspects of operation. As the main institution and environment for implementing educational activities, the effectiveness of school management organization has a direct impact and even a decisive role on the quality of education. Therefore, how to improve the quality management of school education has become a hot topic in the education industry. The education quality management evaluation in higher education institutions is viewed as the multiple-attribute decision-making (MADM) issue. In this paper, the interval-valued neutrosophic number cross-entropy (IVNN-CE) technique is built under interval-valued neutrosophic sets (IVNSs) based on the traditional cross-entropy technique. Then, combine traditional cross-entropy technique with IVNSs, the IVNN-CE technique is constructed for MADM under IVNSs. Finally, the numerical example for education quality management evaluation in higher education institutions was constructed and some comparisons is employed to verify advantages of IVNN-CE technique. The main contribution of this paper is constructed: (1) the cross-entropy model is extended to IVNSs; (1) the CRITIC technique is employed to construct the attribute weights under IVNSs; (3) the IVNN-CE technique is constructed to manage the MADM under IVNSs; (4) a case study about education quality management evaluation in higher education institutions is constructed to show the built technique; (5) some comparative algorithms are constructed to verify the rationality of IVNN-CE technique.

Grey relational analysis method for multi-attribute group decision making based on cumulative prospect theory under single-value neutrosophic sets

In this paper, the author propose a unique multi-attribute group decision making(MAGDM) method SVN-CPT-GRA. The method takes the single-value neutrosophic environment as the decision-making environment and uses the entropy weighted-grey relational analysis method under cumulative prospect theory. First, based on the evaluation of decision-makers, the single-value neutrosophic decision matrix was obtained. The entropy weight method was used to calculate the attribute weights. Next, according to the distance between each SVNN and the negative ideal value, combining the gray relation analysis and the cumulative prospect theory, the correlation between each solution and the attribute is compared to determine the advantages and disadvantages of each solution. Finally, the extended gray relational analysis method is demonstrated to be effectively applied to the decision-making process through a case study of investment choices in new energy vehicles and a comparison with other methods. The main innovations in this paper can be summarized as follows. Firstly, combining the cumulative prospect theory with the gray relational analysis for decision making can better reflect and represent the psychological changes and risk sensitivity of decision makers. Secondly, the entropy weight method is used to determine the attribute weights according to the distance between SVNN and the negative ideal value, which makes the attribute weights more objective and ensures the scientificity and reasonableness of the attribute weights. Thirdly, applying GRA method to the single-value neutrosophic environment, the original simple and practical GRA method to be more widely applied to the fuzzy environment, expanding the scope of application. Overall, the extended GRA method proposed in this paper can be more efficiently and scientifically adapted to MAGDM in fuzzy environments, providing more choices for decision-makers.

Fuzzy Inference Full Implication Method Based on Single Valued Neutrosophic t-representable t-norm: Purposes, Strategies, and a Proof-of-Principle Study


 As a generalization of intuitionistic fuzzy sets, single-valued neutrosophic sets have certain advantages in solving indeterminate and inconsistent information. In this paper, we study the fuzzy inference full implication method based on single-valued neutrosophic t-representable t-norm. Firstly, single-valued neutrosophic fuzzy inference triple I principles for fuzzy modus ponens and fuzzy modus tollens are given. Then, single-valued neutrosophic R-type triple I solutions for FMP and FMT are given. Finally, the robustness of the full implication triple I method based on the left-continuous single-valued neutrosophic t-representable t-norm is investigated. As a special case of the main results, the sensitivity of full implication triple I solutions based on three special single-valued neutrosophic t-representable t-norms are given.

An indeterminacy fusion of encoder-decoder network based on neutrosophic set for white blood cells segmentation

Medical image analysis, particularly the segmentation of White Blood Cells (WBCs), holds critical importance in scrutinizing the quantity and morphology of these cells in smear images, a pivotal step in disease detection. Existing methodologies often fall short in differentiating between healthy and diseased WBCs, emphasizing color components over internal organizational nuances and external morphologies. This paper presents a pioneering contribution through the introduction of an encoder-decoder deep neural network with an indeterminacy fusion-based model explicitly designed for WBC extraction from blood images. In contrast to prior studies, our approach addresses the inadequacies by delving into the intricacies of WBC structure, characterizing object indeterminacy within the neutrosophic set domain. The encoder-decoder network is fortified by integrating WBC indeterminacy as a fusion component, enabling the segmentation of WBCs into distinct nucleus and cytoplasm regions. The efficacy of our methodology is evaluated across three datasets with varying resolutions. Quantitative metrics such as segmentation accuracy and intersection over union (IoU) are employed to assess the proposed network's performance, which consistently outperforms three original encoder-decoder networks. Notably, our model achieves commendable precision rates, with the highest mean segmentation accuracy reaching 0.95301 across the three datasets. These results underscore the enhanced performance of our segmentation network, attributing its success to the influential role of indeterminacy fusion in augmenting conventional segmentation methods. In summary, this work not only introduces a novel solution for WBC segmentation but establishes its superiority over existing methods. The interpretive insights gained from the results highlight the potential of indeterminacy fusion to drive advancements in the realm of medical image segmentation, emphasizing originality, significance, and superior performance metrics.

The Energy of Interval-Valued Complex Neutrosophic Graph Structures: Framework, Application and Future Research Directions


 Graph structure is a developing field with many real-world applications and advancements, particularly effective frameworks for integrative problem-solving in computer networks and artificial intelligence systems. To define the idea of an Interval-Valued Complex Neutrosophic Graph Structure (IVCNGS), the concept of an Interval-Valued Complex Neutrosophic Set (IVCNS) is applied to the graph structure. Using the adjacency matrix to calculate the degree of vertex, we have defined some findings about the IVCNGS. Further, we compute the energy and Laplacian energy of IVCNGS. Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of IVCNGS, and we have discussed their application in IVCNGS. Finally, we develop an algorithm that clarifies the fundamental processes of the application.

A Combined Compromise Solution (CoCoSo) of MCDM Problems for Selection of Medical Best Bearing Ring

Bearings offers a variety of products designed to meet the rigorous requirements of the medical sector for patient safety, such as diagnostic and laboratory equipment, surgical and dental instruments, ventilators, heart pumps, etc. In the field of medical instruments, the bearing rings compromise from superior quality metals to perform surgical operations safely. The selection of the best bearing ring materials for medical applications is a critical task that involves considering various factors to ensure optimal performance, reliability, and safety. The study explores challenges and criteria in selecting the ideal bearing ring for medical devices and equipment. The criteria discussed encompass material compatibility, biocompatibility, lubrication requirements, precision, cleanliness, durability, noise and vibration control, size and dimension, load capacity, temperature and environmental conditions, regulatory compliance, manufacturing considerations, compatibility with adjacent components, maintenance, and serviceability. The challenges mainly include biocompatibility validation, material selection, performance requirements, regulatory compliance, size limitations, cost considerations, supply chain reliability, long-term stability, maintenance, expertise, and collaboration. To address the current challenges of medical bearing the study needs to understand the medical requirements, and engagement with trusted suppliers and regulatory bodies. The study presents a multi-criteria decision-making methodology (MCDM) problem with various criteria and alternatives with uncertainty conditions. The decision maker’s perspectives evaluate the importance of criteria and alternatives. The neutrosophic set is used to deal with uncertainty conditions. The study illustrates a solution to select the best bearing ring to ensure the success and safety of medical applications. The MCDM provides solutions to choose the best bearing ring. A Combined Compromised Solution (CoCoSo) method is used as an MCDM method with neutrosophic theory to select the best alternatives. A numerical case study is presented to show the applicability and availability of the proposed methodology.

Tconns: a novel time-varying context-aware offloading strategy for mobile edge computing

Mobility is a fundamental feature of mobile edge computing. Due to the mobility of users, the contextual attributes of cloudlets such as server resources and network state will dynamically change with time during offloading, showing time-varying and fuzzy characteristics. To this end, how to make efficient offloading decision to provide low-latency, low-power and highly reliable services in MEC has become a critical issue. In this paper, we propose a time-varying context-aware cloudlet decision algorithm based on neutrosophic set, TConNS {text {(The Code of TConNS is available at https://github.com/zhengLabs/NSO)}}. Firstly, we establish a representation model of the multi-dimensional time-varying context of candidate cloudlets, including the mobile residence time. Secondly, we adopt the backward generator of cloud model theory to transform the contextual raw data into a single-valued neutrosophic set with the expression ability for fuzzy information. Finally, we use a series of appropriate operations under the own unique computing system of neutrosophic set to obtain the best cloudlet. Extensive experiments show that TConNS reduces the average response time by about 49% and the average energy consumption by about 46%, and also reduces the number of task failures.

Evaluating Blockchain Cybersecurity Based on Tree Soft and Opinion Weight Criteria Method under Uncertainty Climate

In the era of digital transformation (DT), many digital technologies have emerged and have had a positive impact on society. Nevertheless, because of certain issues with existing technologies, innovative technology has developed to eradicate them. Fog computing (FC) plays a vital role as an intermediate between edge layer and cloud computing (CC) to resolve limited resources and capabilities. In the same vein, blockchain technology (BCT) is responsible for resolving privacy and security issues that IoT suffers from. Due to using cryptography rules and hashing which is utilized in BCT to prevent any trickery. Hence, BC shows promise as a possible remedy for the cybersecurity issue, especially in financial services and transactions. In the context of cybersecurity, it's critical to comprehend how financial sector businesses might handle these issues by investigating the use of BCT for financial transactions. Thereby, we constructed Tree Soft Evaluator (TrSEV) framework to evaluate security for enterprises (ENs) that embrace BCT as a cyber security method. The initial and important step in the evaluation process is determining the influenced criteria. In our problem, we modeled the determined criteria of BCT in Tree soft (TrSo) model. After that these criteria are analyzed and obtaining weights for it. Hence, we harnessed Opinion Weight Criteria Method (OWCM) as a novel multi-criteria decision-making (MCDM) technique to obtain criteria weights, and weighted sum model (WSM) is utilized for ranking enterprises and recommending optimal and worst enterprise. Finally, the techniques harnessed in our constructed framework are employed under the authority of Neutrosophic theory, precisely Single value Neutrosophic sets (SVNSs).

T-Spherical Fuzzy-Valued Neutrosophic Set Theory

From fuzzy to neutrosophy, multiple hybrid models have been innovated, with each introduced model surpassing its predecessor. Due to the inherent indeterminacy in the world, a more precise form of imprecision is required. As a result, more sophisticated variants of the neutrosophic set have been created. Examples of these amalgamations include fuzzy neutrosophic sets, intuitionistic fuzzy neutrosophic sets, Pythagorean fuzzy neutrosophic sets, neutrosophic vague sets, and neutrosophic rough sets. The main objective of this paper is to present another variant of the neutrosophic set called T-spherical fuzzy-valued neutrosophic set (T-SFVNS). Serving as a generalization of the aforementioned combinations, T-SFVNS allows for the representation of indeterminacy and inconsistency in a more nuanced manner. In this paper, we define the T-SFVNS and Tspherical fuzzy-valued neutrosophic numbers (T-SFVNNs). Additionally, we propose several types of score and accuracy functions to compare the T-SFVNNs. We also present the basic operations of T-SFVNSs and the algebraic operations of T-SFVNNs, supported by proofs and illustrative examples..

Robots selection for sine trigonometric (l1, l2, l3) neutrosophic sets using different aggregation operators

This article discusses a new approach to multiple attribute decision-making (MADM) based on sine trigonometric (ST) (l1, l2, l3) neutrosophic sets (NS). We discuss the concept of ST (l1, l2, l3) neutrosophic weighted averaging (NWA), ST (l1, l2, l3) neutrosophic weighted geometric (NWG), ST (l1, l2, l3) generalized neutrosophic weighted averaging (GNWA) and ST (l1, l2, l3) generalized neutrosophic weighted geometric (GNWG). We presented during our discussion showed an algorithm that used these operators. Extensive Hamming distances are illustrated numerically. Also included in this communication are discussions of idempotency, boundness, commutativity, and monotonicity for ST (l1, l2, l3) neutrosophic sets. By using them, you can find the best option faster, easier, and more conveniently. As a result, ST (l1, l2, l3) and more precise conclusions are more closely related. A comparison is made between some current models and those proposed to demonstrate the dependability and utility of the current models. Furthermore, fascinating findings were revealed in the study.