Error Measures Research Articles

Energy-Dependent, Self-Adaptive Mesh h(p)-Refinement of a Constraint-Based Continuous Bubnov-Galerkin Isogeometric Analysis Spatial Discretization of the Multi-Group Neutron Diffusion Equation with Dual-Weighted Residual Error Measures

Energy-dependent self-adaptive mesh refinement algorithms are developed for a continuous Bubnov-Galerkin spatial discretization of the multi-group neutron diffusion equation using NURBS-based isogeometric analysis (IGA). The spatially self-adaptive algorithms employ both mesh (h) and polynomial degree (p) refinement. Constraint-based equations are established across irregular interfaces with hanging-nodes; they are based upon master-slave relationships and the conservative interpolation between surface meshes. A similar Galerkin projection is employed in the conservative interpolation between volume meshes to evaluate group-to-group source terms over energy-dependent meshes; and to evaluate interpolation-based error measures. Enforcing continuity over an irregular mesh does introduce discretization errors. However, local mesh refinement allows for a better allocation of computational resources; and thus, more accuracy per degree of freedom. Two a posteriori interpolation-based error measures are proposed. The first heuristically minimizes local contributions to the discretization error, which becomes competitive for global quantities of interest (QoIs). However, for localized QoIs, over energy-dependent meshes, certain multi-group components may become under-resolved. The second employs duality arguments to minimize important error contributions, which consistently and reliably reduces the error in the QoI.

Uncontrolled pain: a call for better study design.

Studies assessing animal pain in veterinary research are often performed primarily for the benefit of animals. Frequently, the goal of these studies is to determine whether the analgesic effect of a novel treatment is clinically meaningful, and therefore has the capacity to improve the welfare of treated animals. To determine the treatment effect of a potential analgesic, control groups are necessary to allow comparison. There are negative control groups (where pain is unattenuated) and positive control groups (where pain is attenuated). Arising out of animal welfare concerns, there is growing reluctance to use negative control groups in pain studies. But for studies where pain is experimentally induced, the absence of a negative control group removes the opportunity to demonstrate that the study methods could differentiate a positive control intervention from doing nothing at all. For studies that are controlled by a single comparison group, the capacity to distinguish treatment effects from experimental noise is more difficult; especially considering that pain studies often involve small sample sizes, small and variable treatment effects, systematic error and use pain assessment measures that are unreliable. Due to these limitations, and with a focus on farm animals, we argue that many pain studies would be enhanced by the simultaneous inclusion of positive and negative control groups. This would help provide study-specific definitions of pain and pain attenuation, thereby permitting more reliable estimates of treatment effects. Adoption of our suggested refinements could improve animal welfare outcomes for millions of animals globally.

Reliability and validity of cross‑culturally adapted oral health‑related quality‑of‑Life instruments for Brazilian children and adolescents: a systematic review

Objective This systematic review aimed to review the reliability and validity of oral health-related quality of life (OHRQoL) questionnaires for Brazilian children and adolescents. Also, the cross-cultural adaptation was evaluated.Methods This systematic review is registered in PROSPERO (CRD42022300018) and was performed based on the COSMIN guideline. Electronic searches were performed in the PubMed/MEDLINE, Web of Science, Lilacs, BVS (BIREME), Scielo, and Embase databases until March 2023 by two independent reviewers. There was no restriction on time or language. The following studies were included: validation studies and cross-cultural adaptation of OHRQoL instruments into Brazilian Portuguese; studies that evaluated the measurement properties of OHRQoL questionnaires in children and adolescents and that reported at least one of the measurement properties: reliability, internal consistency, error measurement, content validity, construct validity, criterion validity, discriminant validity, and/or convergent validity. The following were excluded: studies of systematic reviews of OHRQoL measures; studies reporting OHRQoL assessment through instruments; construction (development) and validation of a new instrument; questionnaires that had a single item; and validation for Portuguese from Portugal. The cross-cultural adaptation process and psychometrics of the included studies were verified.Results 6556 articles were identified, and 19 manuscripts were included. All studies were conducted in Brazil, and the age of the participants ranged from 2 to 15.42 years old. Sixteen articles presented the cross-cultural validation steps. Cronbach's alpha of the revised instruments ranged from 0.59 to 0.86.ConclusionsIt can be concluded that most studies provided information and evidence regarding validity, reliability, translation, and cultural adaptation.

Role of ultrasensitivity in biomolecular circuitry for achieving homeostasis

Living systems have developed control mechanisms for achieving homeostasis. Here, we propose a plausible biological feedback architecture that exploits ultrasensitivity and shows adaptive responses without requiring error detection mechanism (i.e., by measuring an external reference signal and deviation from this). While standard engineering control systems are usually based on error measurements, this is not the case for biological systems. We find that a two-state negative feedback control system, without explicit error measurements, is able to track a reference signal that is implicitly determined by the tunable threshold and slope characterizing the sigmoidal ultrasensitive relationship implemented by the control system. We design different ultrasensitive control functions (ultrasensitive up- or down-regulation, or both) and, by performing sensitivity analysis, show that increasing the sensitivity level of the control allows achieving robust adaptive responses to the effects of parameter variations and step disturbances. Finally, we show that the devised control system architecture without error detection is implemented within the yeast osmoregulatory response network and allows achieving adaptive responses to osmotic stress, by exploiting the ubiquitous ultrasensitive features of the involved biomolecular circuitry.

Distribution State Estimation and Its Impact of Load Modeling

To maintain system security and other essential parameters like reliability and quality, continuous monitoring of the system is very important. Considering the distribution network, state estimation (SE) methods can be adopted. The purpose of the method is to identify and estimate unknown variables based on the online measurements of test data. The primary objectives considered in this paper are: To choose the exact SE method and the artificial neural network (back propagation algorithm), which can be used for determination in the islanding mode of distribution network states, the composite load model is considered for the estimation of states and further enhancement. By adopting the system, state variables in terms of error are measured in the 12-bus distribution network with precise measurements and compared with practical values. The SE proposed includes results with the load flow backward-forward sweep method to satisfy the system state variables. Numerical results indicate that the model performs better for error measurement data with states and in the case of state forecasting.

Lq-norm multiple kernel fusion regression for self-cleansing sediment transport

Experimental and modeling studies have been conducted to develop an approach for self-cleansing rigid boundary open channel design such as drainage and sewer systems. Self-cleansing experiments in the literature are mostly performed on circular channel cross-section, while a few studies considered self-cleansing sediment transport in small rectangular channels. Experiments in this study were carried out in a rectangular channel with a length of 12.5 m, a width of 0.6 m, a depth of 0.7 m and having an automatic control system for regulating channel slope, discharge and sediment rate. Behind utilizing collected experimental data in this study, existing data in the literature for rectangular channels are used to develop self-cleansing models applicable for channel design. Through the modeling procedure, this study recommends Lq-norm multiple kernel fusion regression (LMKFR) techniques for self-cleansing sediment transport. The LMKFR is a regression technique based on the regularized kernel regression method which benefits from the combination of multiple information sources to improve the performance using the Lq-norm multiple kernel learning framework. The results obtained by LMKFR are compared to support vector regression benchmark and existing conventional regression self-cleansing sediment transport models in the literature for rectangular channels. The superiority of LMKFR is illustrated in an accurate modeling as compared with its alternatives in terms of various statistical error measurement criteria. The encouraging results of LMKFR can be linked to utilization of several kernels which are fused effectively using an Lq-norm prior that captures the intrinsic sparsity of the problem at hand. Promising performance of LMKFR technique in this study suggests it as an effective technique to be examined in similar environmental, hydrological and hydraulic problems.

A remote self-calibration design for three-phase power monitoring terminal

In view of the situation that the existing three-phase power metering device is prone to excessive error and inaccurate measurement during long-term operation, and the device must be removed for re-calibration, a self-calibration power monitoring terminal based on NB-IOT communication is proposed. The power monitoring terminal adopts an external voltage transformer and current transformer, and the input signal is mV and mA level AC small signal. The integrated design of single-chip microcomputer and metering chip is used in the power monitoring terminal. The single-chip microcomputer reads and writes the data collected by the metering chip and displays and transmits the power data. After the remote measurement instruction is issued, the three-phase sinusoidal signal generator chip inside the system is used to simulate the voltage signal and current model, and the external voltage and current input channel are switched with the analog signal channel through the analog switch to complete the internal self-verification work of the device. This scheme can significantly reduce the workload caused by dismantling, installing and verifying the instrument, ensure the measurement accuracy of the instrument for a long time, and has great practical value.

Thermal Error Measurement and Compensation with Torque Limit Skip in Swiss-type Lathe Manufacturing

This paper presents a new methodology for the measurement of thermal errors of Swiss-type lathes. The basis of the proposed method is the torque limit skip function integrated in the lathe’s control which stops the motion of a linear axis if the torque on the corresponding axis servo is exceeded. The skip signal is triggered via a slow contact between a bar in the lathe’s spindle and an artefact in the lathe’s tool holder. Experimental results indicate that when a sufficiently low torque override limit is applied, the axis positioning repeatability under the repeated application of the torque limit skip is within ±1μm. The relative change in position of the axis after the skip measured over several hours is the thermal error which can be compensated. The proposed measurement technique offers significant advantages over conventional thermal error measurement with a touch-trigger probe or linear displacement sensors: if available on the machine’s control, it does not require any specialized installation, can be used during production, and delivers comparable results without high additional equipment costs.

Aquila Optimizer-Based Hybrid Predictive Model for Traffic Congestion in an IoT-Enabled Smart City

Effective traffic congestion prediction is need of the hour in a modern smart city to save time and improve the quality of life for citizens. In this study, AB_AO (ARIMA Bi-LSTM using Aquila optimizer), a hybrid predictive model, is proposed using the most effective time-series data prediction statistical model ARIMA (Autoregressive Integrated Moving Average) and sequential predictive Deep Learning (DL) technique LSTM (Long Short-Term Memory) which helps in traffic congestion prediction with a minimum error rate. Also, the Aquila optimizer (AO) is used to elevate the adequacy of the AB_AO model. Three road traffic datasets of different cities from the “CityPulse EU FP7 project” are used to implement the proposed hybrid model. In a time-series dataset, two components need to be handled with care, i.e., linear and nonlinear. In this study, the ARIMA model has been used to manage linear components and Bi-LSTM is used to handle nonlinear components of the time-series dataset. The Aquila Optimizer (AO) is used for hyperparametric tuning to enhance the performance of Bi-LSTM. Error measurement parameters like the Mean Absolute Error (MAE), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE) are used to validate the results. A detailed mathematical and empirical analysis is given to justify the performance of the AB_AO model using an ablation study and comparative analysis. The AB_AO model acquires more stable and precise results with MSE as 18.78, MAE as 3.18, and MAPE as 0.21 than other models. It may further help to predict the vehicle count on the road, which may be of great help in reducing wastage of time in traffic congestion.

Fractional-Order Fuzzy PID Controller with Evolutionary Computation for an Effective Synchronized Gantry System

Gantry-type dual-axis platforms can be used to move heavy loads or perform precision CNC work. Such gantry systems drive a single axis with two linear motors, and under heavy loads, a high driving force is required. This can generate a pulling force between the drive shafts in the coupling mechanism. In these situations, when a synchronization error becomes too large, mechanisms can become deformed or damaged, leading to damaged equipment, or in industrial settings, an additional power consumption. Effectively and accurately acquiring the synchronized movement of the platform is important to reduce energy consumption and optimize the system. In this study, a fractional-order fuzzy PID controller (FOFPID) using Oustaloup’s recursive filter is used to control a synchronous X–Y gantry-type platform. The optimized controller parameters are obtained by the measurement of control errors in a simulated environment. Four optimization methods are tested and compared: particle swarm optimization, invasive weed optimization, a gray wolf optimizer, and biogeography-based optimization. The systems were tested and compared in order to optimize the control parameters. Each of the four algorithms is simulated on four contour shapes: a circle, bow, heart, and star. The simulations and control scheme of the experiments are implemented using MATLAB, and the reference paths were planned using non-uniform rational B-splines (NURBS). After running the simulations to determine the optimal control parameters, each set of acquired control parameters is also tested and compared in the experiments and the results are recorded. Both the simulations and experiments show good results, and the tracking of the X–Y platform showed improved performance. Two performance indices are used to determine and validate the relative performance of the models and results.

Measurement of focal plane error in laser powder bed fusion machines

Amongst the many sub-systems that make up laser powder bed fusion (PBF-LB) machines, the optomechanical sub-system stands out due to its potential for off-nominal performance but incommensurate level of study on performance evaluation. Nominally, the optomechanical system focuses the laser onto a planar field which is at a controlled position and orientation relative to the powder bed. Deviations from this assumed condition, sometimes referred to as defocus or focus offset, have the potential to significantly impact the manufacturing process by influencing the energy intensity at the process zone. Herein, a novel, high-throughput, low-cost, artifact-based methodology to measure focus offset is detailed. In a single continuous build process, tracks at varying offsets from the build plane were created by ablating the coating on discrete coupons located throughout the build area. By examining these track widths, the focus offset was determined at a relatively fine spatial resolution over the build space, down to 25 mm intervals along the x and y directions, thus ascertaining the discrepancy between the laser focal plane and the build plane, i.e., focal plane error. Results were found to agree with reference measurements to within 0.27 mm over the entire build space and defocus levels ranging from approximately -1.6 to 1.7 mm were discovered. Field sag and optomechanical misalignment were the major casual factors. It is concluded that similar or more severe levels of defocus may be present in the typical PBF-LB machine, which may impart considerable impacts to the overall PBF-LB process.

Gear Integrated Error Determination Using the Gaussian Template Convolution-Facet Method

A gear integrated error, a combination of individual and composite errors, carries richer information and has long been a key target of classic gear error measurement techniques. However, in the age of intelligent manufacturing, the classic methods for gear integrated error measurement are no longer able to meet the emerging requirements of large-scale gears and real-time online measurement. To address this gap, a novel approach to obtaining the gear integrated error based on GTC−Facet (Gaussian template convolution-Facet) is proposed. This method accurately pinpoints the sub-pixel contour of gears in images, enabling a quick derivation of the gear integrated error curve. From this curve, other individual and composite errors can be analyzed. The gear error information obtained through our method has higher measurement accuracy, achieving a positioning accuracy of 3.6 μm for the gear profile. Moreover, during the measurement process, the measured gear remains unclamped, and the entire measurement process can be completed within 0.35 s, which is much faster than classic methods. Our method meets the demands of online measurements and provides a new avenue for gear error measurement.

Validity and reliability of the English version of the Diabetic Foot Self-Care Questionnaire: a cross-cultural adaptation.

The objective of this study was to carry out the cross-cultural adaptation and validation of the Diabetic Foot Self-Care Questionnaire into the English language, broadening the applicability of this patient-reported outcome measure and improving the monitoring of patients with diabetic foot disease. The validation study into English was conducted in two phases: cross-cultural adaptation and psychometric validation study. Short Form-12 Version 2, EuroQoL-5D and Foot Function Index were used to analyze the criterion validity. Item response, internal consistency, standard error of measurement, minimal detectable change and construct validity were calculated in the validation phase. An English version of the questionnaire (DFSQ-UMA-En) was successfully obtained. A total of n = 193 participants were tested to confirm the validity and reliability of the questionnaire. Internal consistency values ranged from very good to excellent (Cronbach's α =0.889-0.981), and reliability was excellent (ICC = 0.854-0.959). Standard error measurement value was =2.543. Criterion validity ranged from r = 0.429 to r = 0.844. For construct validity, Kaiser-Meyer-Olkin test was =0.752. DFSQ-UMA-En is a valid and reliable tool with good readability and comprehension features. This questionnaire addresses foot self-care behaviors in patients with diabetic foot disease, standing out as essential for early diagnosis and prevention strategies in clinical and research settings.

The state of renewable energy source envelopes in urban areas

Several computational algorithms have been developed to determine building heating and cooling energy requirements on a citywide scale. However, limited contemporary models can analyse all structures in an urban region, and even fewer can handle power consumption on monthly basis or at lower levels. Nevertheless, these characteristics are crucial for urban power generation planners. In light of the imperative role that accurate modelling plays in evaluating urban energy systems, this paper underscores the critical need to overcome the substantial processing costs associated with existing models, recognizing that addressing this challenge is pivotal for precise simulation of urban electricity consumption and, consequently, for informing effective urban power generation planning strategies. This study delves into the integration of solutions related to renewable energy source envelopes, focusing particularly on the strategic approach within clusters of buildings in urban energy systems. The primary objective of this research is to elucidate the cluster methodology and its defining parameters, followed by an exploration of key influencing factors and modelling methodologies. The study is delimited by specific considerations encompassing barrier dimensions, methodological intricacies, and the pivotal elements that govern renewable energy source envelope-based power provisions for building clusters. According to the conducted analysis, the processing costs of these models are a significant hurdle to accurate microsimulation of urban electricity consumption. Theoretical and numerical approximations should be used; even computational methodologies are subject to uncertainty analysis and error measurement.

Differential disruption of response alternation by precipitated Δ9-THC withdrawal and subsequent Δ9-THC abstinence in mice

In addition to overt somatic symptoms, cannabinoid withdrawal can also manifest as disruptions in motivation and attention. Experimental animal models using operant-conditioning approaches reveal these differences, in either antagonist-precipitated or spontaneous withdrawal models. However, these processes have yet to be characterized in the same subjects simultaneously. To differentiate between motivational and attentional processes disrupted in cannabinoid withdrawal, the current study used a response alternation task in which a fixed-ratio (FR) schedule repeatedly alternated between two spatially distinct response options throughout daily training sessions. This task yielded traditional measures of motivation (e.g., response latency) as well as attention (e.g., responses to the incorrect side). After two weeks of training, male and female C57BL/6 J mice either received vehicle or Δ9-THC (10 mg/kg, s.c.) twice daily for 5 days. On the 6th day, all mice received their final injection of vehicle or Δ9-THC followed 30 min later by injection of the CB1 receptor selective inverse agonist rimonabant (2 mg/kg, i.p.) to precipitate withdrawal. Testing continued for 3 days post-rimonabant to assess how THC abstinence impacted task performance. Whereas rimonabant decreased response rates to equal degrees in THC-treated and vehicle-treated mice, THC-treated mice showed longer session times, longer response latencies, and more errors per reinforcer. Only THC-treated mice showed a longer latency to switch after committing an error reflecting that precipitated withdrawal impacted measures of both motivation and attention. During the 3-day abstinence window, performance of vehicle-treated mice returned to baseline, but THC-treated mice continued to show disruptions in motivational measures. Importantly, attentional measures (errors and latency to switch after an error) were unaffected by THC abstinence. These data suggest that precipitated and “spontaneous” cannabinoid withdrawal may be qualitatively and quantitatively distinct withdrawal conditions with precipitated withdrawal disrupting both attentional and motivational processes, while abstinence may only affect motivation.

Identifying and Exploring the Impact Factors for Intraocular Pressure Prediction in Myopic Children with Atropine Control Utilizing Multivariate Adaptive Regression Splines.

The treatment of childhood myopia often involves the use of topical atropine, which has been demonstrated to be effective in decelerating the progression of myopia. It is crucial to monitor intraocular pressure (IOP) to ensure the safety of topical atropine. This study aims to identify the optimal machine learning IOP-monitoring module and establish a precise baseline IOP as a clinical safety reference for atropine medication. Data from 1545 eyes of 1171 children receiving atropine for myopia were retrospectively analyzed. Nineteen variables including patient demographics, medical history, refractive error, and IOP measurements were considered. The data were analyzed using a multivariate adaptive regression spline (MARS) model to analyze the impact of different factors on the End IOP. The MARS model identified age, baseline IOP, End Spherical, duration of previous atropine treatment, and duration of current atropine treatment as the five most significant factors influencing the End IOP. The outcomes revealed that the baseline IOP had the most significant effect on final IOP, exhibiting a notable knot at 14 mmHg. When the baseline IOP was equal to or exceeded 14 mmHg, there was a positive correlation between atropine use and End IOP, suggesting that atropine may increase the End IOP in children with a baseline IOP greater than 14 mmHg. MARS model demonstrates a better ability to capture nonlinearity than classic multiple linear regression for predicting End IOP. It is crucial to acknowledge that administrating atropine may elevate intraocular pressure when the baseline IOP exceeds 14 mmHg. These findings offer valuable insights into factors affecting IOP in children undergoing atropine treatment for myopia, enabling clinicians to make informed decisions regarding treatment options.

A comparative investigation of a time‐dependent mesh method and physics‐informed neural networks to analyze the generalized Kolmogorov–Petrovsky–Piskunov equation

AbstractThe Kolmogorov–Petrovsky–Piskunov (KPP) partial differential equation (PDE) is solved in this article using the moving mesh finite difference technique (MMFDM) in conjunction with physics‐informed neural networks (PINNs). We construct a time‐dependent mesh to obtain approximate solutions for the KPP problem. The temporal derivative is discretized using a backward Euler, while the spatial derivatives are discretized using a central implicit difference scheme. Depending on the error measure, several moving mesh partial differential equations (MMPDEs) are employed along the arc‐length and curvature mesh density functions (MDF). The proposed strategy has been suggested to yield remarkably precise and consistent results. To find the approximate solution, we additionally employ physics‐informed neural networks (PINNs) to compare the outcomes of the adaptive moving mesh approach. It has been observed that solutions obtained using the moving mesh method (MMM) are sufficiently accurate, and the absolute error is also much lower than the PINNs.

Revising the core knowledge confusions scale: a measure of logical error associated with cognitive and personality traits

AbstractThe Core Knowledge Confusions scale (CKC) was designed to predict paranormal and spiritual beliefs, alternative health beliefs and the degree to which people assign meaning to events. It measures the likelihood of individuals' tendency to accept ontologically confused content as literally true and has been used to investigate beliefs such as the paranormal. However, the psychometric properties of the CKC have not been tested, limiting the scale’s practical utility. The CKC was revised and tested, internal consistency was checked, and associations to paranormal belief were assessed using a panel survey of 1010 Australian residents (Mage = 52, SD = 17.69, Female = 56%). Using structural equation modelling and regression, the revised scale (CKC-R) content deviated from previous findings. However, it demonstrated acceptable internal, construct, and divergent validity. External correlates of the CKC-R were aligned with expectations: associating with high verbal knowledge, an intuitive cognitive style, and the absorption personality trait (i.e., a tendency to experience altered states of consciousness). The CKC-R provides researchers with a validated measure predicting paranormal belief that is associated with both cognitive and personality-based traits. Interpretation of the CKC-R as a measure of ontological error is less clear and requires further investigation.

Individual In-Situ GPS-Derived Acceleration-Speed Profiling: Toward Automatization and Refinement in Male Professional Rugby Union Players

BackgroundRecently a proof-of-concept was proposed to derive the soccer players’ individual in-situ acceleration-speed (AS) profile from global positioning system (GPS) data collected over several sessions and games. The present study aimed to propose an automatized method of individual GPS-derived in-situ AS profiling in a professional rugby union setting.MethodAS profiles of forty-nine male professional rugby union players representing 61.5 million positions, from which acceleration was derived from speed during 51 training sessions and 11 official games, were analyzed. A density-based clustering algorithm was applied to identify outlier points. Multiple AS linear relationships were modeled for each player and session, generating numerous theoretical maximal acceleration (A0), theoretical maximal running speed (S0) and AS slope (ASslope, i.e., overall orientation of the AS profile). Each average provides information on the most relevant value while the standard deviation denotes the method accuracy. In order to assess the reliability of the AS profile within the data collection period, data were compared over two 2-week phases by the inter-class correlation coefficient. A0 and S0 between positions and type of sessions (trainings and games) were compared using ANOVA and post hoc tests when the significant threshold had been reached.ResultsAll AS individual profiles show linear trends with high coefficient of determination (r2 > 0.81). Good reliability (Inter-class Correlation Coefficient ranging from 0.92 to 0.72) was observed between AS profiles, when determined 2 weeks apart for each player. AS profiles depend on players’ positions, types of training and games. Training and games data highlight that highest A0 are obtained during games, while greatest S0 are attained during speed sessions.ConclusionsThis study provides individual in-situ GPS-derived AS profiles with automatization capability. The method calculates an error of measurement for A0 and S0, of paramount importance in order to improve their daily use. The AS profile differences between training, games and playing positions open several perspectives for performance testing, training monitoring, injury prevention and return-to-sport sequences in professional rugby union, with possible transferability to other sprint-based sports.Key PointsAS profiles computed from rugby union GPS data provide positional benchmarks during training and competition.This study provides automatic detection of atypical data and the computation of error measurement of theoretical maximal acceleration and speed components.This refinement constitutes a step forward for a daily use of ecological data by considering data collection and method reliabilities.This easy-to-implement approach may facilitate its use to the performance management process (talent identification, training monitoring and individualization, return-to-sport).

Strong (α, k)-cut and computational-based segmentation based novel hesitant fuzzy time series forecasting model

Hesitant fuzzy set (HFS) is an ideal tool to deal with hesitancy situation arises due to collection of membership values for each time series datum. Many researchers developed HFS based fuzzy time series forecasting (FTSF) models in past years. In this article, a novel method is proposed to deal with critical factors affecting the HFS based FTSF and name as strong (α,k)-cut and computational-based segmentation based hesitant fuzzy time series forecasting (SCS-FTSF). Computational-based segmentation (CBS) approach is developed to determination of number of intervals and generating intervals. Proposed method uses Gaussian and triangular membership functions to construct HFS and uses aggregation operator aggregating the membership values to construct aggregate HFS. A novel fuzzification procedure is proposed by taking all aggregate HFSs with non-zero aggregated membership value relative to data points. Strong(α,k)-cut is employed to selection of suitable aggregate HFLRs. Further, a defuzzification approach is also proposed to obtaining numerical value. In order to assess the performance of proposed SCS -FTSF method two time series datasets are used. Results of error measures and validation tests confirms that superiority of the proposed SCS-FTSF method.