Fuzzy Clustering Method Research Articles

Unsupervised clustering of longitudinal clinical measurements in electronic health records.

Longitudinal electronic health records (EHR) can be utilized to identify patterns of disease development and progression in real-world settings. Unsupervised temporal matching algorithms are being repurposed to EHR from signal processing- and protein-sequence alignment tasks where they have shown immense promise for gaining insight into disease. The robustness of these algorithms for classifying EHR clinical data remains to be determined. Timeseries compiled from clinical measurements, such as blood pressure, have far more irregularity in sampling and missingness than the data for which these algorithms were developed, necessitating a systematic evaluation of these methods. We applied 30 state-of-the-art unsupervised machine learning algorithms to 6,912 systematically generated simulated clinical datasets across five parameters. These algorithms included eight temporal matching algorithms with fourteen partitional and eight fuzzy clustering methods. Nemenyi tests were used to determine differences in accuracy using the Adjusted Rand Index (ARI). Dynamic time warping and its lower-bound variants had the highest accuracies across all cohorts (median ARI>0.70). All 30 methods were better at discriminating classes with differences in magnitude compared to differences in trajectory shapes. Missingness impacted accuracies only when classes were different by trajectory shape. The method with the highest ARI was then used to cluster a large pediatric metabolic syndrome (MetS) cohort (N = 43,426). We identified three unique childhood BMI patterns with high average cluster consensus (>70%). The algorithm identified a cluster with consistently high BMI which had the greatest risk of MetS, consistent with prior literature (OR = 4.87, 95% CI: 3.93-6.12). While these algorithms have been shown to have similar accuracies for regular timeseries, their accuracies in clinical applications vary substantially in discriminating differences in shape and especially with moderate to high missingness (>10%). This systematic assessment also shows that the most robust algorithms tested here can derive meaningful insights from longitudinal clinical data.

Segmenting hotspots from medical thermal images using Density-based modified FC-Pc FS with spatial information

ABSTRACT Thermal cameras complemented with robust and automated computational intelligence-aided diagnostic systems can be deployed at public gathering points and on smartphones to raise alarms about thriving diseases of their body due to inflammation in a timely manner, thereby strengthening human health systems. In this work, we have proposed two robust Density-based modified Picture Fuzzy Clustering methods with spatial information to segment hotspots from human’s abnormal thermal images. We formulated and solved the objective function by combining P c FS-based clustering method with modified Renyi’s Entropy. We demonstrated the robustness of our methods, DSIFC-Pc FS and DSIMFC-Pc FS, on three publicly available datasets and an artificially created noisy dataset of thermal images. We have obtained a ZC score of 0.933, 0.947 and 0.933 for DB-DMR-IR, DB-FOOT-IR and DB-THY-IR datasets, respectively. Also, our method converged to an optimal partition matrix in minimum iterations. The experimental performance shows that the proposed approaches, DSIFC- P c FS and DSIMFC- P c FS, outperformed other ten related approaches in segmenting the medical thermal images with and without noise, indicating their robustness and efficacy, in terms of various unsupervised evaluation metrics. Also, we statistically analysed their performance in contrast to other methods using the Friedman Test, which advocate their superiority.

One-Step Multiview Fuzzy Clustering With Collaborative Learning Between Common and Specific Hidden Space Information.

Multiview data are widespread in real-world applications, and multiview clustering is a commonly used technique to effectively mine the data. Most of the existing algorithms perform multiview clustering by mining the commonly hidden space between views. Although this strategy is effective, there are two challenges that still need to be addressed to further improve the performance. First, how to design an efficient hidden space learning method so that the learned hidden spaces contain both shared and specific information of multiview data. Second, how to design an efficient mechanism to make the learned hidden space more suitable for the clustering task. In this study, a novel one-step multiview fuzzy clustering (OMFC-CS) method is proposed to address the two challenges by collaborative learning between the common and specific space information. To tackle the first challenge, we propose a mechanism to extract the common and specific information simultaneously based on matrix factorization. For the second challenge, we design a one-step learning framework to integrate the learning of common and specific spaces and the learning of fuzzy partitions. The integration is achieved in the framework by performing the two learning processes alternately and thereby yielding mutual benefit. Furthermore, the Shannon entropy strategy is introduced to obtain the optimal views weight assignment during clustering. The experimental results based on benchmark multiview datasets demonstrate that the proposed OMFC-CS outperforms many existing methods.

Framework for Regional to Global Extension of Optical Water Types for Remote Sensing of Optically Complex Transitional Water Bodies

Water quality indicator algorithms often separate marine and freshwater systems, introducing artificial boundaries and artifacts in the freshwater to ocean continuum. Building upon the Ocean Colour- (OC) and Lakes Climate Change Initiative (CCI) projects, we propose an improved tool to assess the interactions across river–sea transition zones. Fuzzy clustering methods are used to generate optical water types (OWT) representing spectrally distinct water reflectance classes, occurring within a given region and period (here 2016–2021), which are then utilized to assign membership values to every OWT class for each pixel and seamlessly blend optimal in-water algorithms across the region. This allows a more flexible representation of water provinces across transition zones than classic hard clustering techniques. Improvements deal with expanded sensor spectral band-sets, such as Sentinel-3 OLCI, and increased spatial resolution with Sentinel-2 MSI high-resolution data. Regional clustering was found to be necessary to capture site-specific characteristics, and a method was developed to compare and merge regional cluster sets into a pan-regional representative OWT set. Fuzzy clustering OWT timeseries data allow unique insights into optical regime changes within a lagoon, estuary, or delta system, and can be used as a basis to improve WQ algorithm performance.

Fuzzy Adaptive Knowledge-Based Inference Neural Networks: Design and Analysis.

A novel fuzzy adaptive knowledge-based inference neural network (FAKINN) is proposed in this study. Conventional fuzzy cluster-based neural networks (FCBNNs) suffer from the challenge of a direct extraction of fuzzy rules that can capture and represent the interclass heterogeneity and intraclass homogeneity when the data possess complex structures. Moreover, the capability of the cluster-based rule generator in FCBNNs may decrease with the increase of data dimensionality. These drawbacks impede the generation of desired fuzzy rules, and affect the inference results depending on the fuzzy rules, thereby limiting their generalization ability. To address these drawbacks, an adaptive knowledge generator (AKG), consisting of the observation paradigm (OP) and clustering strategy (CS), is effectively designed to improve the generalization ability in FAKINN. The OP distills the characteristic information (CI) from data to highlight the homogeneity and heterogeneity of objects, and the CS, viz., the weighted condition-driven fuzzy clustering method (WCFCM), is proposed to summarize the CI to construct fuzzy rules. Moreover, the feedback between the OP and CS can control the dimensionality of CI, which endows FAKINN with the potential to tackle high-dimensional data. The main originality of the study focuses on the AKG and WCFCM that are proposed to develop the structural design methodology of FNNs. The performance of FAKINN is evaluated on various benchmarks with 27 comparative methods, and two real-world problems are adopted to validate its effectiveness. Experimental results show that FAKINN outperforms the comparison methods.

Surface water monitoring from 1984 to 2021 based on Landsat time-series images and Google Earth Engine

Dynamic monitoring of surface water bodies is essential for understanding global climate change and the impact of human activities on water resources. Satellite remote sensing is characterized by large-scale monitoring, timely updates, and simplicity, and it has become an important means of obtaining the distribution of surface water bodies. This study is based on a long time-series Landsat satellite images and the Google Earth Engine (GEE) platform, focusing on Anhui Province in China, and proposes a method for extracting surface water that combines water indices, Bias-Corrected Fuzzy Clustering Method (BCFCM), and OTSU threshold segmentation. The spatial distribution of surface water in Anhui Province was obtained from 1984 to 2021, and further analysis was conducted on the spatiotemporal characteristics of surface water in each city and three major river basins within the province. The results indicated that the overall accuracy of water extraction in this study was 94.06 %. Surface water in Anhui was most abundant in 1998 and least in 2001, with more distribution in the south than in the north. Northern Anhui is dominated by rivers, while southern Anhui has more lakes. Permanent surface water with an inundation frequency of above 75 % covered approximately 4341 km2, accounting for 32.03 % of the total water, while seasonal water with an inundation frequency between 5 % and 75 % covered about 6661 km2, accounting for 49.15 % of the total water, others were considered temporary surface water. By comparing our results with the global annual surface water released by the Joint Research Centre (JRC), we found that our study performed better in extracting lakes and rivers in terms of completeness, but the extraction results for aquaculture areas were slightly less than the JRC dataset. Overall, the long-term surface water dataset established in this study can effectively supplement the existing datasets and provide important references for regional water resource investigation, management, as well as flood monitoring.

Grouping Districts / Cities in Central Sulawesi Province Based on Poverty Indicators Using the Fuzzy Geographically Weighted Clustering -Artificial Bee Colony Method

Introduction: Poverty is the main problem that is the focus of attention of the government in Indonesia. In general, poverty is a person's inability to meet basic basic needs in every aspect of life. Cluster analysis is a solution to map this problem. Method: Fuzzy Geographically Weighted Clustering-Artificial Bee Colony (FGWC-ABC) is one clustering method that is an integration of classical fuzzy clustering methods and geodemographic elements. Artificial Bee Colony is a metaheuristic algorithm that is used as a global optimization to increase cluster accuracy. Artificial Bee Colony can efficiently and effectively solve various function optimization problems in various cases. Result and Discussion: The research results obtained 3 optimum clusters with each cluster characteristic relatively different based on poverty indicators. Cluster 1 with low poverty, cluster 2 with high poverty, and cluster 3 with moderate poverty. Conclusion: By using the IFV validity index, 3 optimum clusters were obtained with different characteristics of each cluster based on its indicators. Cluster 1 consists of three regencies/cities with low poverty status, cluster 2 consists of seven regencies/cities with high poverty status, and cluster 3 consists of six regencies/cities with moderate poverty status.

Fuzzy C-Means Algorithm Modification Based on Distance Measurement for River Water Quality

River water quality could be determined by understanding the capacity of pollutants in a water body. Fuzzy C-Means (FCM) is one of the fuzzy clustering methods for determining river water quality by measuring water quality parameters, that is, dissolved oxygen (DO) and total dissolved solids (TDS). The FCM algorithm is an effective fuzzy clustering algorithm for grouping data but often produces local and inconsistent optimal solutions due to the partition matrix's random initialisation process. Therefore, this study proposes to modify the FCM algorithm to be precise in the partition matrix initialisation process using several distance concepts. The purpose of the proposed algorithm modification is to get more consistent FCM clustering results and minimise stop iterations. The validation process for the clustering results uses the FCM algorithm, and the FCM modification algorithm uses three parameters, namely the Partition Coefficient Index (PCI), Partition Entropy Index (PEI) and Silhouette Score (SS). The experiments were conducted with three replications and using various distance concepts. The results showed that the number of iterations stopped in the FCM algorithm has different values for PCI, PEI, SS, and stop iterations and objective functions in each trial. On the contrary, the FCM modification algorithm has consistent PCI, PEI, and SS values, and the number of iterations stops with fewer iterations. Therefore, the modified algorithm for initialising the partition matrix can be used in the fuzzy C-means clustering algorithm.

Two-stage multi-objective evolutionary algorithm for overlapping community discovery.

As one of the essential topological structures in complex networks, community structure has significant theoretical and application value and has attracted the attention of researchers in many fields. In a social network, individuals may belong to different communities simultaneously, such as a workgroup and a hobby group. Therefore, overlapping community discovery can help us understand and model the network structure of these multiple relationships more accurately. This article proposes a two-stage multi-objective evolutionary algorithm for overlapping community discovery problem. First, using the initialization method to divide the central node based on node degree, combined with the cross-mutation evolution strategy of the genome matrix, the first stage of non-overlapping community division is completed on the decomposition-based multi-objective optimization framework. Then, based on the result set of the first stage, appropriate nodes are selected from each individual's community as the central node of the initial population in the second stage, and the fuzzy threshold is optimized through the fuzzy clustering method based on evolutionary calculation and the feedback model, to find reasonable overlapping nodes. Finally, tests are conducted on synthetic datasets and real datasets. The statistical results demonstrate that compared with other representative algorithms, this algorithm performs optimally on test instances and has better results.

MDEFC: Automatic recognition of human activities using modified differential evolution based fuzzy clustering method

In the present scenario, automatic Human Activity Recognition (HAR) is an emerging research topic, particularly in the applications of healthcare, Human Computer Interaction (HCI), and smart homes. By reviewing existing literature, the majority of the HAR methods achieved limited performance, while trained and tested utilizing unseen Internet of Things (IoT) data. In order to achieve higher recognition performance in the context of HAR, a new clustering method named Modified Differential Evolution based Fuzzy Clustering (MDEFC) is proposed in this article. The proposed MDEFC method incorporates an asymptotic termination rule and a new differential weight for enhancing the termination condition and improving this method’s ability in exploring the solution space of the objective function. The extensive empirical analysis states that the proposed MDEFC method achieved impressive recognition results with minimal training time by using both spatial and temporal features of the individual. The proposed MDEFC method’s effectiveness is tested on a real time dataset and an online Wireless Sensor Data Mining (WISDM) v1.1 dataset. The result findings demonstrate that the proposed MDEFC method averagely obtained 99.73 % of precision and 99.86 % of recall on the WISDM v1.1 dataset. Similarly, the proposed MDEFC method averagely obtained 93.46 % of f1-measure, 94.60 % of recall, and 93.88 % of precision on the real time dataset. These obtained experimental results are significantly higher in comparison to the traditional HAR methods.

Robust Picture Fuzzy Regression Functions Approach Based on M-Estimators for the Forecasting Problem

AbstractA picture fuzzy regression function approach is a fuzzy inference system method that uses as input the lagged variables of a time series and the positive, negative and neutral membership values obtained by picture fuzzy clustering method. In a picture fuzzy regression functions method, the parameter estimation is also obtained by ordinary least squares method. Since the picture fuzzy regression functions approach is based on the ordinary least squares method, the forecasting performance decreases when there are outliers in the time series. In this study, a picture fuzzy regression function approach that can be used even in the presence of outliers in a time series is proposed. In the proposed method, the parameter estimation for the picture fuzzy regression function approach is performed based on robust regression with Bisquare, Cauchy, Fair, Huber, Logistic, Talwar and Welsch functions. The forecasting performance of the proposed method is evaluated on the time series of the Spanish and the London stock exchange time series. The forecasting performance of these time series are evaluated separately for both the original and outlier cases. Besides, the proposed method is compared with several different fuzzy regression function approaches and a neural network method. Based on the results of the analysis, it is concluded that the proposed method outperforms the other methods even when the time series contains both original and outliers.

Artificial intelligence schemes to predict the mechanical performance of lignocellulosic fibers with unseen data to enhance the reliability of biocomposites

PurposeThis work introduces an integrated artificial intelligence schemes to enhance accurately predicting the mechanical properties of cellulosic fibers towards boosting their reliability for more sustainable industries.Design/methodology/approachFuzzy clustering and stacked method approach were utilized to predict the mechanical performance of the fibers. A reference dataset contains comprehensive information regarding mechanical behavior of the lignocellulosic fibers was compiled from previous experimental investigations on mechanical properties for eight different fiber materials. Data encompass three key factors: Density of 0.9–1.6 g/cm3, Diameter of 5.9–1,000 µm, and Microfibrillar angle of 2–49 deg were utilized. Initially, fuzzy clustering technique was utilized for the data. For validating proposed model, ultimate tensile strength and elongation at break were predicted and then examined against unseen new data that had not been used during model development.FindingsThe output results demonstrated remarkably accurate and highly acceptable predictions results. The error analysis for the proposed method was discussed by using statistical criteria. The stacked model proved to be effective in significantly reducing level of uncertainty in predicting the mechanical properties, thereby enhancing model’s reliability and precision. The study demonstrates the robustness and efficacy of the stacked method in accurately estimating mechanical properties of lignocellulosic fibers, making it a valuable tool for material scientists and engineers in various applications.Originality/valueCellulosic fibers are essential for biomaterials to enhance developing green sustainable bio-products. However, such fibers have diverse characteristics according to their types, chemical composition and structure causing inconsistent mechanical performance. This work introduces an integrated artificial intelligence schemes to enhance accurately predicting the mechanical properties of cellulosic fibers towards boosting their reliability for more sustainable industries. Fuzzy clustering and stacked method approach were utilized to predict the mechanical performance of the fibers.

Modeling of machine tool thermal error based on factor extraction

Abstract In the process of modeling thermal errors in machine tools, optimizing the extraction of temperature information affects the prediction accuracy of the thermal error model. This paper proposes a thermal error modeling method based on factor extraction. Firstly, the temperature measurement points are optimized to determine the optimal number using finite element, fuzzy clustering, and correlation methods. Then, the common deformation factors in the machine tool temperature information are extracted through factor analysis, and they are used as independent variables for thermal error modeling. Finally, the method was applied to establish a model for thermal error model for a certain model of precision machine tool, and a regression model of the machine tool was obtained after factor extraction optimization, the effectiveness and feasibility of the proposed method in this paper were verified by comparing it with experimental data. The method proposed in this study provides a reference for modeling thermal errors in various types of machine tools in the future.

Estimation curve of multivariate adaptive biresponse fuzzy clustering means regression splines approach to stunting and wasting cases in Southeast Sulawesi

This article offers a new method of clustering data. This method is constructed by combining the multivariate adaptive regression spline biresponse continuous model (MARSBC) with the fuzzy clustering means (FCM) approach, called the multivariate adaptive biresponse fuzzy clustering means regression splines (MABFCMRS) model. This method uses patterns obtained from the MARSBC model to separate data into specific groups. Observing unobserved heterogeneity that has not been obtained from previous models. Unlike the classic fuzzy clustering methods that use euclid distances to determine the weight of the object, this method uses the total square of the massed residual distance generated by the MARSBC model. Theoretical studies were conducted to obtain predictions for the MABFCMRS model parameters. Furthermore, this method was applied to stunting and wasting cases in southeastern Sulawesi province. The results of the research show that in the case of stunting modeling and wasting in southeast Sulawesi province, the best clusters were obtained based on the criteria of partition coefficient (PC) and modification of PC (MPC). This research is able to show that the clustering process using the MABFCMRS model has been able to improve generalized cross-validation (GCV) values and determination coefficients.•This paper presents a new, effective method for clustering data based on unobserved heterogeneity.•This is applicable to sizable samples with 3 to 20 predictors.

Intelligent optimal layout of drainage pipe network monitoring points based on information entropy theory

The rapid expansion of urban drainage pipe networks, driven by economic development, poses significant challenges for efficient monitoring and management. The complexity and scale of these networks make it difficult to effectively monitor and manage the discharge of urban domestic sewage, rainwater, and industrial effluents, leading to illegal discharges, leakage, environmental pollution, and economic losses. Efficient management relies on a rational layout of drainage pipe network monitoring points. However, existing research on optimal monitoring point layout is limited, primarily relying on manual analysis and fuzzy clustering methods, which are prone to human bias and ineffective monitoring data. To address these limitations, this study proposes a coupled model approach for the automatic optimization of monitoring point placement in drainage pipe networks. The proposed model integrates the information entropy index, Bayesian reasoning, the Monte Carlo method, and the stormwater management model (SWMM) to optimize monitoring point placement objectively and measurably. The information entropy algorithm is utilized to quantify the uncertainty and complexity of the drainage pipe network, facilitating the identification of optimal monitoring point locations. Bayesian reasoning is employed to update probabilities based on observed data, while the Monte Carlo method generates probabilistic distributions for uncertain parameters. The SWMM is utilized to simulate stormwater runoff and pollutant transport within the drainage pipe network. Results indicate that (1) the relative mean error of the parameter inversion simulation results of the pollution source tracking model is linearly fitted with the information entropy. The calculation shows that there is a good positive linear correlation between them, which verifies the feasibility of the information entropy algorithm in the field of monitoring node optimization; (2) the information entropy algorithm can be well applied to the optimal layout of a single monitoring node and multiple monitoring nodes, and it can correspond well to the inversion results of the tracking model parameters; (3) the constructed monitoring point optimization model can well realize the optimal layout of monitoring points of a drainage pipe network. Finally, the pollution source tracking model is used to verify the effectiveness of the optimal layout of monitoring points, and the whole process has less human participation and a high degree of automation. The automated monitoring point optimization layout model proposed in this study has been successfully applied in practical cases, significantly improving the efficiency of urban drainage network monitoring and reducing the degree of manual participation, which has important practical significance for improving the level of urban water environment management.

Road dynamic landscape design and simulation based on fuzzy clustering algorithm

Against the backdrop of rapid economic growth and continuous expansion of road networks in China, the planning, design, greening, and beautification of roads at all levels have entered a systematic implementation phase. Particularly noteworthy is the emergence of dynamic road landscape design as a major focus in the research on urban road beautification in the new era. This paper proposes a road dynamic landscape optimization design scheme based on the fuzzy clustering algorithm. It analyzes the primary elements constituting dynamic road landscapes and summarizes the fundamental principles for designing such landscapes. The fuzzy clustering method is employed to classify different road landscapes, optimizing the design system. Through simulation experiments, the effectiveness of the proposed scheme is validated, with results indicating an 8.34% higher accuracy compared to traditional methods. The study suggests that such road design not only meets basic traffic needs but also achieves greening and beautification effects while catering to users visual and psychological needs, showcasing the unique cultural, historical, and lifestyle characteristics of the city. Furthermore, this design fosters harmonious integration between roads and their ancillary structures and surrounding buildings, significantly improving the citys landscape and living environment.

Functional Optical Coherence Tomography of Rat Cortical Neurovascular Activation during Monopulse Electrical Stimulation with the Microelectrode Array

This paper presents a study to evoke rat cortical functional activities, including hemodynamic and neural tissue signal changes, by monopulse electrical stimulation with a microelectrode array using functional optical coherence tomography (fOCT). Based on the principal component analysis and fuzzy clustering method (PCA-FCM), the hemodynamic response of different size blood vessels in rat cortex are analyzed, showing that the hemodynamic response of the superficial large blood vessels is more concentrated. In the regions of neural tissue where blood vessels are removed, positive significant pixels (the intensity of the pixel for five consecutive frames is greater than the average value plus triple standard deviation) and negative significant pixels (the intensity of the pixel for five consecutive frames is less than the average value minus triple standard deviation) exist, and the averaged intensity signal responds rapidly with an onset time of ~20.8 ms. Furthermore, the hemodynamic response was delayed by ~3.5 s from the neural tissue response. fOCT can provide a label-free, large-scale and depth-resolved map of cortical neurovascular activation, which is a promising technology to monitor cortical small-scale neurovascular activities.

FUZZY INTERACTIVE CLUSTERING METHOD

The article examines an example of a system in which a large number of short texts are generated. In it, participants create strategic planning documents, within which key performance indicators are determined. The formulations of key performance indicators form a data set consisting of short texts. Within the framework of this system, there is an urgent task of forming and updating a classifier based on this set. A solution to this problem is presented using the fuzzy interactive clustering method. This method allows expert to perform clustering sets of short texts, issuing reverse communication based on the results of each step interactive clustering. Collection procedure reverse does not imply any connection availability of an expert special knowledge about work neural network and is assembled in human-readable form matrices reverse communications. Such an approach has advantages over clustering methods requiring adjustments metaparameters algorithm not related directly with the clustering results. Also important advantage the proposed method is opportunity realize clustering sets data related to various language domains that do not match the domain on which was produced education language models, due to proposed extension method dictionary language models This property allows use the proposed algorithm in a narrow way specialized domains, as well as in domains that do not allow you to obtain a full-fledged corpus of texts for yourself training language models.

Short-term PV power data prediction based on improved FCM with WTEEMD and adaptive weather weights

Photovoltaic (PV) systems are commonly used in zero energy buildings(ZEBs) due to their high efficiency and convenience. However, PV systems are affected by meteorological factors with nonlinearities and stochasticity in the power generation process, which leads to inaccurate prediction of PV power, affects the relationship between energy supply and user demand, and then has a significant impact on the stability of PV grid connection. To address these challenges, this paper proposes a WTEEMD-FCM-IGWO-LSTM method for the numerical prediction of PV power. Firstly, for the noise interference in the meteorological data of PV power generation collected from PV power stations, this paper proposes an Ensemble Empirical Mode Decomposition (EEMD) method based on the wavelet threshold algorithm improvement (WTEEMD) for noise reduction and reconstruction of meteorological data to enhance the signal-to-noise ratio in the data. Secondly, considering the stochastic nature of unstable meteorological factors, an improved fuzzy C-mean clustering (FCM) method is employed to classify the PV power process dataset and enhance the correlation between meteorological factors and power data. Subsequently, prediction models for the power values of the PV power generation process under each of the three meteorological conditions are developed using Long Short-Term Memory (LSTM) based on the classified sample data. Finally, the proposed model is evaluated through simulation using historical Australian PV data. The experimental results show that it is possible to accurately predict the power of PV power generation, improve the utilization of clean energy, and support the sustainable development of ZEBs.

A fuzzy Gaussian process regression function approach for forecasting problem

A fuzzy regression function approach is a fuzzy inference system method whose rules cannot be determined based on expert opinion, unlike a classical fuzzy inference system. In a fuzzy regression function approach, an input matrix consists of memberships obtained by the fuzzy clustering method and lagged variables of the time series. In the fuzzy regression function approach, the output vector corresponding to this input matrix is also created and the parameter estimation for the method is carried out with the ordinary least square method. As it is known, the ordinary least square method assumes that the data are linear. In addition, although it is very useful to include a priori information describing the formation of the data in the model, in most cases this information is not available. It is also inappropriate to use a model that does not accurately characterize the data. However, it is not appropriate to estimate parameters for nonlinear data using the ordinary least square method. One of the methods to be used in such a situation is the Gaussian process regression method. While the parameters of a selected basis function are fitted in the ordinary least squares regression method, how all measured data are related is determined in the Gaussian process regression. Besides, Gaussian process regression is a Bayesian approach, it can provide uncertainty measurements on forecasts. In this study, a fuzzy Gaussian process regression function is proposed. The contribution of this paper is to propose a new fuzzy inference system that can be used to solve nonlinear data by proposing a fuzzy Gaussian process regression function. The performance of the newly proposed method is evaluated based on the closing values of the Bitcoin and Crude oil time series. The performance comparison of the proposed method is evaluated with many different forecasting methods and it is concluded that the proposed method has superior forecasting performance.