Gaussian Membership Function Research Articles

Parameter-coupled state space models based on quasi-Gaussian fuzzy approximation

The accuracy of a fuzzy system’s approximation is closely tied to the performance of fuzzy control systems design, while this system’s interpretability depends on the description of a mechanical model using human language. This research introduces a quasi-Gaussian membership function characterized by a pair of parameters to achieve the sensitivity of a triangular membership function along with the interpretability of Gaussian membership functions. Consequently, a two-dimensional (2-D) quasi-Gaussian membership function is derived, and a method for establishing quasi-Gaussian fuzzy systems (QGFS) using a rectangular grid is proposed. After validating the approximation properties using the sine function for the one-dimensional (1-D) and 2-D QGFS, the systems are applied to approximate the depyrogenation tunnel, a significant piece of equipment in the pharmaceutical industry with various mechanical designs. Validation results indicate that the 1-D and 2-D QGFS can achieve an approximation error varying within a ± 5% range. Meanwhile, the 1-D and 2-D QGFSs are applied to mechanical models of the depyrogenation tunnel with satisfactory final approximation results. Lastly, the 2-D QGFS is capable of demonstrating an excellent description of models with coupled parameters.

Design and application of interval type-2 fuzzy neural network systems optimized with hybrid algorithms

Interval type-2 fuzzy neural network systems (IT2 FNNSs) own the advantages of IT2 fuzzy logic systems (FLSs) and NN. The paper designs a kind of IT2 FNNSs for permanent magnetic drive (PMD) forecasting. For each rules of IT2 FNNSs, whose antecedents, consequents and input measurements are chosen as Gaussian IT2 membership functions (MFs). The proposed hybrid backpropagation (BP) algorithms and recursive least square (RLS) algorithms are adopted to tune all the parameters simultaneously. Simulation instances on the basis of data of permanent magnetic drive (PMD) torque and revolutions per minute (rpm) are adopted for testing the performances of proposed hybrid optimized IT2 FNNSs for forecasting. Convergence analysis illustrates that the IT2 FNNSs have excellent generalization capability compared with both singleton and non-singleton T1 FNNSs.

Efficient parameter estimation in biochemical pathways: Overcoming data limitations with constrained regularization and fuzzy inference

In analytical modeling for biochemical pathways, precisely determining unknown parameters is paramount. Traditional methods, reliant on experimental time course data, often encounter roadblocks — limited accessibility and variable quality — that can significantly impact the algorithm’s performance. In this study, we address these hurdles by unveiling a groundbreaking parameter estimation technique, Constrained Regularized Fuzzy Inferred Extended Kalman Filter (CRFIEKF). This innovative approach eliminates the need for experimental time-course measurements and capitalizes on the existing imprecise relationships among the molecules within the network. Our proposed framework integrates a Fuzzy Inference System (FIS) block to encapsulate these approximated relationships. To fine-tune the estimated parameter values, we employ Tikhonov regularization. The selection of Tikhonov regularization and Gaussian membership functions was based on the Mean Squared Error (MSE) values observed during the parameter estimation process, contrasting our results with those of previous studies.We rigorously tested the proposed approach across various pathways, from the glycolytic processes in mammalian erythrocytes and yeast cells to the intricate JAK/STAT and Ras signaling pathways. The results were impressive, showing a significant similarity (p-value < 0.001) to the outcomes of specific prior experiments. The dynamics of the biochemical networks normalized within the [0, 1] range mirrored the transient behavior (MSE < 0.5) of both in vivo and in silico results from previous studies. In conclusion, our findings highlight the effectiveness of CRFIEKF in estimating the kinetic parameter values without prior knowledge of experimental data within a biochemical pathway in the state-space model. The proposed method underscores its potential as a game-changer in biochemical pathway analysis.

A risk assessment of inhibited cargo operations in maritime transportation: a case of handling styrene monomer

Hazardous cargo handling on tanker ships involves various risks that could lead to accidents such as explosion and fire. Investigating these risks is crucial to safeguard life, property and the marine environment. This paper performs a risk assessment specific to hazardous cargoes with special requirements. It addresses the risks of inhibited cargo operation, which has not been adequately studied in the literature despite its criticality. Styrene monomer is selected as the inhibited cargo type since failures during its handling may lead to polymerisation and catastrophic consequences. Using the Failure Modes, Effects and Criticality Analysis (FMECA) 24 failures are identified, and their occurrence, severity and detection aspects are evaluated by experts familiar with the process. In addition, a rule-based fuzzy logic technique with Gaussian membership functions is employed to support the traditional FMECA application. The integration of methods helps to deal with the limitations of FMECA in the calculation of risk priority number (RPN). Based on the fuzzy RPN results, failure modes are prioritized and preventive actions are presented for the high-ranked failure modes. The outputs of the study could help to increase the awareness of operators and interested individuals concerning the risks of tanker cargo operations with special requirements.

An Enhanced Fuzzy Hybrid of Fireworks and Grey Wolf Metaheuristic Algorithms

This research work envisages addressing fuzzy adjustment of parameters into a hybrid optimization algorithm for solving mathematical benchmark function problems. The problem of benchmark mathematical functions consists of finding the minimal values. In this study, we considered function optimization. We are presenting an enhanced Fuzzy Hybrid Algorithm, which is called Enhanced Fuzzy Hybrid Fireworks and Grey Wolf Metaheuristic Algorithm, and denoted as EF-FWA-GWO. The fuzzy adjustment of parameters is achieved using Fuzzy Inference Systems. For this work, we implemented two variants of the Fuzzy Systems. The first variant utilizes Triangular membership functions, and the second variant employs Gaussian membership functions. Both variants are of a Mamdani Fuzzy Inference Type. The proposed method was applied to 22 mathematical benchmark functions, divided into two parts: the first part consists of 13 functions that can be classified as unimodal and multimodal, and the second part consists of the 9 fixed-dimension multimodal benchmark functions. The proposed method presents better performance with 60 and 90 dimensions, averaging 51% and 58% improvement in the benchmark functions, respectively. And then, a statistical comparison between the conventional hybrid algorithm and the Fuzzy Enhanced Hybrid Algorithm is presented to complement the conclusions of this research. Finally, we also applied the Fuzzy Hybrid Algorithm in a control problem to test its performance in designing a Fuzzy controller for a mobile robot.

Two-stage approach for COVID-19 vaccine supply chain network under uncertainty using the machine learning algorithms: A case study

Healthcare systems worldwide have been facing a scarcity in COVID-19 vaccine rationing as a severe challenge. This research presents a two-stage optimization mathematical model to design a COVID-19 vaccine supply chain network under uncertain demand and lead time. The first stage aims to minimize the lead time by focusing on the suppliers' goals. In contrast, four objective functions, namely minimization of the gap of service level, the waiting time in the queue, and costs, and maximization of the related assignment, are considered in the second stage considering the government's goals. The popular supervised machine learning approaches are adopted to estimate COVID-19 vaccine demand. The boosted neural networks method as a superior mechanism is selected to estimate the demand as input parameters to the model. Additionally, since the lead time is an inherently uncertain parameter, a fuzzy method by Gaussian membership function is employed. Then, a rolling horizon planning mechanism along with an iterative procedure is proposed to prevent the shortage of vaccines. The applicability of the proposed model and solution method is demonstrated based on a real-case study from Iran. The results indicate that when demand exceeds supply, priority grouping becomes essential. Additionally, fairly allocating vaccines among people is a severe challenge during an epidemic, and preferences among the government and suppliers can make the problem more complex. The computational results illustrate that implementing the proposed model and approaches achieves the goals and reduces the shortage in the network compared to the existing condition.

Control of quadrotor robot via optimized nonlinear type-2 fuzzy fractional PID with fractional filter: Theory and experiment

This paper presents a novel approach for controlling quadrotor robots. It introduces an optimized nonlinear fractional order type-2 fuzzy system integrated with a Fractional Order Proportional-Integral-Derivative controller, supplemented by a fractional filter in the derivative section. The input scaling factors, which represent the scaling coefficients associated with the input variables of the fuzzy system, are adjusted using nonlinear gains. The proposed controller combines type-2 fuzzy logic, fractional calculus, and nonlinear gains to enhance the control performance of the system. Its purpose is to provide superior control accuracy, robustness, and disturbance rejection capabilities. In order to enhance the performance of the quadrotor, the Bat Optimization Algorithm is utilized to finely adjust the controller parameters and membership function parameters of the fuzzy system. The fuzzy system incorporates Gaussian membership functions and applies the Mamdani min-max method for inference, utilizing the centroid method for defuzzification. The performance of the controller is evaluated in two scenarios: tracking aerial maneuvers in the presence of wind disturbance, and achieving angular stabilization by tracking a pulse function in the Hardware-In-The-Loop real-time test. The findings demonstrate significant improvements compared to traditional PID controllers. These improvements surpass 34 % without a filter and 53 % with a filter, in all directions and scenarios.

Fuzzy Attention Neural Network to Tackle Discontinuity in Airway Segmentation.

Airway segmentation is crucial for the examination, diagnosis, and prognosis of lung diseases, while its manual delineation is unduly burdensome. To alleviate this time-consuming and potentially subjective manual procedure, researchers have proposed methods to automatically segment airways from computerized tomography (CT) images. However, some small-sized airway branches (e.g., bronchus and terminal bronchioles) significantly aggravate the difficulty of automatic segmentation by machine learning models. In particular, the variance of voxel values and the severe data imbalance in airway branches make the computational module prone to discontinuous and false-negative predictions, especially for cohorts with different lung diseases. The attention mechanism has shown the capacity to segment complex structures, while fuzzy logic can reduce the uncertainty in feature representations. Therefore, the integration of deep attention networks and fuzzy theory, given by the fuzzy attention layer, should be an escalated solution for better generalization and robustness. This article presents an efficient method for airway segmentation, comprising a novel fuzzy attention neural network (FANN) and a comprehensive loss function to enhance the spatial continuity of airway segmentation. The deep fuzzy set is formulated by a set of voxels in the feature map and a learnable Gaussian membership function. Different from the existing attention mechanism, the proposed channel-specific fuzzy attention addresses the issue of heterogeneous features in different channels. Furthermore, a novel evaluation metric is proposed to assess both the continuity and completeness of airway structures. The efficiency, generalization, and robustness of the proposed method have been proved by training on normal lung disease while testing on datasets of lung cancer, COVID-19, and pulmonary fibrosis.

Minimum nonprobabilistic entropy deconvolution for fault diagnosis of rolling element bearings

The blind deconvolution methods (BDMs) is one of the most common methods for fault diagnosis of rolling bearings, and it is essential to maintain the safe and reliable operation of mechanical equipment. However, noise interference and the need for prior periods limit the scope of application of the BDMs. In this paper, a new minimum nonprobabilistic entropy deconvolution (MNPED) method is proposed. According to the correlation between fault impact and non-Gaussianity, the Gaussian membership function in fuzzy set theory is used to map the sample points to the membership degree of Gaussian distribution, and then the nonprobabilistic entropy (NPE) is formed to measure the impact characteristics of the signal. Then NPE is incorporated into the iterative process of solving the filter coefficient. Finally, the target signal and the optimal filter coefficient are selected based on the criterion of minimum NPE. MNPED is capable of adaptively extracting the periodic pulse of a signal without requiring prior knowledge of the period, even in the presence of strong noise interference. The effectiveness and robustness of the proposed approach are validated through simulation and experimental data.

Developing an Adaptive Neuro-Fuzzy Inference System for Performance Evaluation of Pavement Construction Projects

This study employs an adaptive neuro-fuzzy inference system (ANFIS) to identify critical success factors (CSFs) crucial for the success of pavement construction projects. Challenges such as construction cost delays, budget overruns, disputes, claims, and productivity losses underscore the need for effective project management in pavement projects. In contemporary construction management, additional performance criteria play a vital role in influencing the performance and success of pavement projects during construction operations. This research contributes to the existing body of knowledge by comprehensively identifying a multidimensional set of critical success performance factors that impact pavement and utility project management. A rigorous literature review and consultations with pavement experts identified sixty CSFs, categorized into seven groups. The relative importance of each element and group is determined through the input of 287 pavement construction specialists who participated in an online questionnaire. Subsequently, the collected data undergo thorough checks for normality, dependability, and independence before undergoing analysis using the relative importance index (RII). An ANFIS is developed to quantitatively model critical success factors and assess the implementation performance of construction operations management (COM) in the construction industry, considering aspects such as clustering input/output datasets, fuzziness degree, and optimizing five Gaussian membership functions. The study confirms the significance of three primary CSFs (financial, bureaucratic, and governmental) and communication-related variables through a qualitative structural and behavioral validation process, specifically k-fold cross-validation. The outcomes of this research hold practical implications for the management and assessment of overall performance indices in pavement construction projects. The ANFIS model, validated through robust testing methodologies, provides a valuable tool for industry professionals seeking to enhance the success and efficiency of pavement construction endeavors.

Rainfall Forecasting Using an Adaptive Neuro-Fuzzy Inference System with a Grid Partitioning Approach to Mitigating Flood Disasters

Hydrometeorological disasters are one of the disasters that often occur in big cities like Semarang. Hydrometeorological disasters that often occur are floods caused by high-intensity rainfall in the area. Early mitigation needs to be done by knowing about future rain. Rainfall data in Semarang City fluctuates, so the Adaptive Neuro-Fuzzy Inference System (ANFIS) method approach is very appropriate. This research will use the Grid Partitioning (GP) approach to produce more accurate forecasting. The data used in this research is daily rainfall observation data from the Meteorology Climatology Geophysics Agency (BMKG). The membership functions used are Gaussian and Generalized Bell. The two membership functions will be compared based on the RMSE and MAPE values to get the best one. The data used in this research is daily rainfall data. Rainfall in Semarang City every month experiences anomalies, which can result in flood disasters. The ANFIS-GP method with a Gaussian membership function is the best, with an RMSE value of 0.0898 and a MAPE of 5.2911. Based on the forecast results for the next thirty days, a rainfall anomaly of 102.53 mm on the thirtieth day could cause a flood disaster.

Exploiting nearest neighbor data and fuzzy membership function to address missing values in classification.

The accuracy of most classification methods is significantly affected by missing values. Therefore, this study aimed to propose a data imputation method to handle missing values through the application of nearest neighbor data and fuzzy membership function as well as to compare the results with standard methods. A total of five datasets related to classification problems obtained from the UCI Machine Learning Repository were used. The results showed that the proposed method had higher accuracy than standard imputation methods. Moreover, triangular method performed better than Gaussian fuzzy membership function. This showed that the combination of nearest neighbor data and fuzzy membership function was more effective in handling missing values and improving classification accuracy.

Fusing Fuzzy Entropy With Gaussian and Exponential Membership Functions Outperforms Traditional Entropy Metrics in Monitoring the Depth of Anesthesia Using a Single Frontal EEG Channel

Fusing Fuzzy Entropy With Gaussian and Exponential Membership Functions Outperforms Traditional Entropy Metrics in Monitoring the Depth of Anesthesia Using a Single Frontal EEG Channel

Optimising building heat load prediction using advanced control strategies and Artificial Intelligence for HVAC system

Amid the dynamic challenges posed by the COVID-19 era, this study offers a nuanced exploration, delving into the complexities of optimising building heat load prediction. This study addresses the imperative challenge of optimising building heat load prediction by implementing advanced control strategies and integrating Artificial Intelligence (AI) into air conditioning systems. The study emphasises the need to design HVAC devices for minimal energy consumption without compromising comfort conditions. The study introduces an intelligent predictive adaptive neuro-fuzzy inference system (ANFIS) model that proves highly capable of accurately predicting HVAC performance outcomes while contributing to the development of a comprehensive dataset. The uncertainty percentage is evaluated across various membership functions, with the trapezoidal membership exhibiting the lowest error rate, followed by the Gaussian membership function. Weather parameters crucial to ventilation efficiency and heat load are examined, leading to the identification of an optimal combination involving 45 % relative humidity, 13 °C dry bulb temperature, and 5 km/h wind speed. The current system demonstrates significant efficiency improvements, with ventilation and heat load rates reaching 93 % and 97 %, respectively, compared to pre-COVID-19 conditions. The findings underscore the importance of considering these parameters in future HVAC designs, particularly in the context of COVID-19 guidelines (75 % and 79 %, respectively).

A Comprehensive Evaluation of Shale Oil Reservoir Quality

To enhance the accuracy of the comprehensive evaluation of reservoir quality in shale oil fractured horizontal wells, the Pearson correlation analysis method was employed to study the correlations between geological parameters and their relationship with production. Through principal component analysis, the original factors were linearly combined into principal components with clear and specific physical meanings, aiming to eliminate correlations among factors. Furthermore, Gaussian membership functions were applied to delineate fuzzy levels, and the entropy weight method was used to determine the weights of principal components, establishing a fuzzy comprehensive evaluation model for reservoir quality. Without using principal component analysis, the correlation coefficient between production and evaluation results for the 40 wells in the Cangdong shale oil field was only 0.7609. However, after applying principal component analysis, the correlation coefficient increased to 0.9132. Field application demonstrated that the average prediction accuracy for the cumulative oil production per kilometer of fractured length over 12 months for the 10 applied wells was 91.8%. The proposed comprehensive evaluation method for reservoir quality can guide the assessment of reservoir quality in shale oil horizontal wells.

Nature-inspired optimal tuning of input membership functions of fuzzy inference system for groundwater level prediction

We present a novel regression algorithm that combines a Fuzzy Inference System (FIS) with a nature-inspired algorithm to predict variations in GroundWater Levels (GWLs). Initially, we considered several input features, including precipitation, temperature, evaporation, relative humidity, soil type, and GWL Lag. A feature importance analysis using regression tree ensemble learning reveals GWL lag as the most relevant feature and soil type as the least relevant. We eliminate features with low importance scores (soil type, temperature, and evaporation) to improve the computational efficiency. Our approach leverages Fuzzy C-Means (FCM) clustering to develop a Sugeno-type FIS with definite clusters. The dataset is clustered based on feature similarity, and Gaussian membership functions are assigned to each cluster. The mapping of each point is controlled by the range and standard deviation of the Gaussian membership functions. We train the model keeping 70% of the dataset, iteratively tuning the parameters of the Gaussian membership function for all clusters through the Invasive Weed Optimization (IWO) algorithm. The performance of the model is then evaluated using the remaining 30% of the datasets. The F-IWO-GWL model accurately predicts GWL fluctuations, achieving a high correlation coefficient (R = 0.89), low normalized root mean square error (nRMSE = 0.18), and minimal bias (bias = 0.08). A comparative analysis involving seventeen benchmark algorithms reveals the superior performance of our algorithm. To ensure a fair comparison, we calculated key metrics including Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected AIC (AICc). The F-IWO-GWL algorithm exhibits the lowest values for AIC, BIC, and AICc among all tested algorithms, suggesting the best goodness-of-fit. This study provides a robust approach for predicting GWL fluctuation, applicable to various groundwater management scenarios. It offers valuable insights for policymakers and stakeholders involved in groundwater management, aiding informed decision-making.

Interval Type-2 Mutual Subsethood Cauchy Fuzzy Neural Inference System (IT2MSCFuNIS)

An interval type-2 (IT2) mutual subsethood Cauchy fuzzy neural inference system has been proposed in this paper. The network architecture consists of 3-layers with all connection weights being IT2 Cauchy fuzzy membership functions (CMFs). The crisp inputs to the system are fuzzified into IT2CMFs with fixed centers and uncertain spreads. The hidden layer represents the rule-based knowledge. The firing degree of the antecedent part of each rule at the hidden layer is computed by aggregating the product of the mutual subsethood similarity measures between the inputs and the connection weights. A volume defuzzification is used to compute the numeric output. A gradient descent back-propagation algorithm is used to train the model. The novelty of the proposed model is threefold. First, is enriching the theory of the mutual subsethood fuzzy neural models by adopting the Cauchy membership function (CMF) as another powerful fuzzy basis function (FBF) rather than the classical choice of Gaussian fuzzy membership functions (GMFs). Second, is the success of computing the mutual subsethood similarity measure between the IT2CMFs and all the model parameters’ updating equations in analytic closed-form formulas, not numerically or approximately. Third, is the ability to extract the type-1 (T1) mutual subsethood Cauchy fuzzy neural inference system (T1MSCFuNIS) with all its analytic closed-form formulas directly as a special case from the general formulas of IT2MSCFuNIS model. Such a novelty makes the proposed model a concrete and effective development of the theory of mutual subsethood fuzzy neural models. Both IT2MSCFuNIS and T1MSCFuNIS models have been tested using different examples from the domains of function approximation, classification, and prediction. The results ensure the efficacy of both models compared with other models reported in the literature.

Investigation on the influence of a new trapezoidal-triangular membership function in IT2FLS with type-reductions for a manufacturing application

The performance of Interval type-2 fuzzy logic system (IT2FLS) can be affected by many factors including the type of reduction methodology followed and the kind of membership function applied. Further, a particular membership function is influenced by its construction, the type of optimisation and adaptiveness applied, and the learning scheme adopted. The available literature lags in providing detailed information about such factors affecting the performance of IT2FLS. In this work, an attempt has been made to comprehensively study the factors affecting the performance of IT2FLS by introducing a new trapezoidal-triangular membership function (TTMF). A real-time application of drilling operation has been considered as an example for predicting temperature of the job, which is considered as one of the key state variables to evaluate. A detailed comparison based on membership functions (MFs) such as triangular membership function (TrMF), trapezoidal membership function (TMF), the newly introduced trapezoidal-triangular membership function (TTMF), semi-elliptic membership function (SEMF), and Gaussian membership function (GMF) has been performed and presented. Further, the average error rate obtained with two “type-reduction” methods such as “Wu-Mendel” uncertainty bounds and Center of sets type reduction (COS TR) has also been discussed. This study provides information for selecting a particular MF and “type reduction” scheme for the implementation of IT2FLS. Also, concludes that MF having fewer parameters such as GMF and SEMF possess significant advantages in terms of computation complexity compared to others.

Cardiac Arrhythmia multiclass classification using optimized FLS-based 3D-CNN

Arrhythmia is the medical term for any irregularities in the normal functioning of the heart. Due to their ease of use and non-invasive nature, electrocardiograms (ECGs) are frequently used to identify heart problems. Analyzing a huge number of ECG data manually by medical professionals uses excessive medical resources. Consequently, identifying ECG characteristics based on machine learning has become increasingly popular. However, these conventional methods have some limitations, including the need for manual feature recognition, complex models, and lengthy training periods. This research offers a unique hybrid POA-F3DCNN method for arrhythmia classification that combines the Pelican Optimisation algorithm with fuzzy-based 3D-CNN (F3DCNN) to alleviate the shortcomings of the existing methods. The POA is applied to hyper-tune the parameters of 3DCNN and determine the ideal parameters of the Gaussian Membership Functions used for FLSs. The experimental results were obtained by testing the performance of five and thirteen categories of arrhythmia classification, respectively, on UCI-arrhythmia and the MIT-BIH Arrhythmia datasets. Standard measures such as F1-score, Precision, Accuracy, Specificity, and Recall enabled the classification results to be expressed appropriately. The outcomes of the novel framework achieved testing average accuracies after ten-fold cross-validation are 98.96 % on the MIT-BIH dataset and 99.4% on the UCI arrhythmia datasets compared to state-of-the-art approaches.

Application of hybrid fuzzy interval-based machine learning models on financial time series - A case study of Taiwan biotech index during the epidemic period.

In recent years, the use of machine learning to predict stock market indices has emerged as a vital concern in the FinTech domain. However, the inherent nature of point estimation in traditional supervised machine learning models leads to an almost negligible probability of achieving perfect predictions, significantly constraining the applicability of machine learning prediction models. This study employs 4 machine learning models, namely BPN, LSTM, RF, and ELM, to establish predictive models for the Taiwan biotech index during the COVID-19 period. Additionally, it integrates the Gaussian membership function MF from fuzzy theory to develop 4 hybrid fuzzy interval-based machine learning models, evaluating their predictive accuracy through empirical analysis and comparing them with conventional point estimation models. The empirical data is sourced from the financial time series of the "M1722 Listed Biotechnology and Medical Care Index" compiled by the Taiwan Economic Journal during the outbreak of the COVID-19 pandemic, aiming to understand the effectiveness of machine learning models in the face of significant disruptive factors like the pandemic. The findings demonstrate that despite the influence of COVID-19, machine learning remains effective. LSTM performs the best among the models, both in traditional mode and after fuzzy interval enhancement, followed by the ELM and RF models. The predictive results of these three models reach a certain level of accuracy and all outperform the BPN model. Fuzzy-LSTM effectively predicts at a 68% confidence level, while Fuzzy-ELM and Fuzzy-RF yield better results at a 95% confidence level. Fuzzy-BPN exhibits the lowest predictive accuracy. Overall, the fuzzy interval-based LSTM excels in time series prediction, suggesting its potential application in forecasting time series data in financial markets to enhance the efficacy of investment analysis for investors.