Multivariate Fuzzy Research Articles

A Multivariate Fuzzy Weighted K-Modes Algorithm with Probabilistic Distance for Categorical Data

Data clustering is a data mining approach that assigns similar data to the same group. Traditionally, cluster similarity considers all attributes equally, but in real-world applications, some attributes may be more important than others. Therefore, this study proposes an algorithm that utilizes multivariate fuzzy weighting to demonstrate the varying importance of each attribute, using a Gini impurity measure for weight assignment. Additionally, the proposed algorithm implements probabilistic distance to reduce sensitivity to noise. Probabilistic distance offers more detailed information and better interpretation than Hamming distance, which ignores attribute positions. Probabilistic distance utilizes information about the attribute’s position within and between clusters. This enhances clustering performance by creating clusters with more similar attributes. Therefore, the proposed Multivariate Fuzzy Weighted K-Modes with Probabilistic Distance for Categorical Data (MFWKM-PD) algorithm, based on the multivariate fuzzy K-modes algorithm, not only considers detailed membership calculations but also considers the varying contributions of attributes and their positions in distance calculation. This study evaluated the proposed MFWKM-PD using several benchmark datasets. The experiments validated that the proposed MFWKM-PD shows promising results compared to other algorithms in terms of accuracy, NMI, and ARI.

An Identification Method for Rotor Axis Orbits based on Enhanced Hierarchical Multivariate Fuzzy Entropy and Extreme Learning Machine

An Identification Method for Rotor Axis Orbits based on Enhanced Hierarchical Multivariate Fuzzy Entropy and Extreme Learning Machine

Multi-output time series forecasting with randomized multivariate Fuzzy Cognitive Maps

Fuzzy Cognitive Maps (FCMs) have become a relevant technique for modeling and forecasting time series due to their advantages in dealing with uncertainty and simulating the dynamics of complex systems. Although numerous univariate and multivariate FCM-based forecasting models have been presented in the literature, one of the still open questions is how to enable FCMs to forecast multivariate time series for multiple-input, multiple-output (MIMO) systems with an efficient learning mechanism. from a computational point of view. This paper suggests a randomized MIMO FCM-based forecasting approach called MO-RHFCM to predict low-dimensional multivariate time series. More specifically, MO-RHFCM is a hybrid model merging the concepts of multivariate fuzzy time series, high order FCM (HFCM), and Echo State Networks (ESN). The structure of MO-RHFCM consists of three layers: input layer, reservoir (internal) layer, and output layer. Only the output layer is trainable using the Least Squares minimization algorithm; hence training the proposed MO-RHFCM method is fast and simple. The weights inside each sub-reservoir are selected randomly and remain fixed during the training process. The obtained results indicate the efficacy and validity of the proposed MO-RHFCM technique compared with some machine learning and deep learning baseline models.

A Simplified Prediction Model of Structural Seismic Vulnerability Considering a Multivariate Fuzzy Membership Algorithm

ABSTRACT Fuzzy decision-making and analytic hierarchical processes are ubiquitously used to predict the seismic damage and vulnerability of building clusters. However, the factors affecting the seismic vulnerability of building structures are diversification, cognitive uncertainty, and complex fuzziness. To probe the impact of multiple fuzzy influencing factors on the vulnerability of regional buildings and the degree of membership between them, the development of a structural vulnerability prediction model based on fuzzy decision-making and a hierarchical system with multiple factors has strong theoretical and practical significance. This study proposes a novel method for rapidly predicting structural vulnerability based on a multivariate fuzzy membership index. Rapid fragility prediction models of fiv4e typical structures considering the multivariate fuzzy membership index are established. A new approach is proposed based on the relationship model between the empirical vulnerability index and seven fuzzy membership parameters. Five types of typical structural vulnerability index rapid prediction innovation models are developed. The new prediction model is compared and verified using the quantitative value of China’s macrointensity standard and the structural seismic loss observation data (98,050 × 104 m2 and 995,000 buildings) of 213 typical earthquakes to establish an empirical vulnerability index belt model. The proposed prediction model comprehensively considers multiple fuzzy membership parameters and the empirical structural earthquake damage database. The model analysis and validation results indicate that the proposed model can be further used for the seismic damage evaluation of typical structures and rapid fragility prediction.

Optimal Design and Modeling of Sustainable Buildings Based on Multivariate Fuzzy Logic

The exemplary design of green buildings incorporates multiple correlated parameters that should be optimally selected and updated to ensure effective energy management and sustainable impact of building architecture on the ecosystem. In this paper, the adaptive modeling and development of such sustainable buildings with several unpredictable and qualitative attributes is implemented with multiple-input multiple-output (MIMO) fuzzy control system. The outputs of the proposed fuzzy corroborated sustainable building paradigm comprise of specific characteristics employed for assessing the optimal performance, viz. energy efficiency, user satisfaction, resources optimization, and environment quality. These diverse system criteria measured using the proposed fuzzy optimization model are plotted against their actual theoretical values for each data case. Furthermore, the sample dataset for the proposed sustainable building model is validated through simulation results in terms of mean absolute error and logarithmic quotient error in the estimation of various fuzzy output variables evolving with the dataset size.

Evolving fuzzy time series for spatio-temporal forecasting in renewable energy systems

Forecasting in Renewable Energy Systems is a challenging problem since their inputs present some uncertainties in the data distribution. On the other hand, there is an increasing volume of information recorded by such systems that can be explored by a forecasting model with the expectation of improved performance. This work introduces e-MVFTS (evolving Multivariate Fuzzy Time Series), an evolving forecasting model based on Fuzzy Time Series, and an evolving clustering method based on TEDA (Typicality and Eccentricity Data Analytics) Framework, which uses multivariate time series in a spatio-temporal context. The model has an adaptation mechanism to deal with changes in the data distribution or concept drifts in data streams. The evolving clustering method is adjusted as the data points arrive and are processed, in an online manner. Its performance is evaluated in the application to problems of solar and wind energy forecasting as well as concept drift events. The model was developed in Python programming language using pyFTS library. To contribute to the replication of all the results, we provide all source codes in a public repository. The good results in the different experiments enable the e-MVFTS model to be used in forecasting problems with streaming data in renewable energy systems.

The Study of Multivariate Fuzzy Neural Scheme in Controlling Temperature during Beer Fermentation

The brewery fermentation process has inherence characteristics of multivariable, seriously nonlinear, uncertain, time-variant and large delay. The given process parameters aren’t traced very well. In this paper, segmented control strategy is used, which is dividing the ferment process into pre-fermentation and post-fermentation period. In each ferment period, strategy of fuzzy neural control based on Multivariate –decoupling is adopted and simulated in MATLAB, the results show the strategy’s validity and practicability in controlling beer ferment.

Distributed Evolutionary Hyperparameter Optimization for Fuzzy Time Series

Time series forecasting is an essential task in the management of Smart Cities and Smart Grids, becoming even more challenging when it needs to deal with big data time series. The development of highly accurate machine learning models is yet harder when considering the optimization of hyperparameters, which is an expensive computational task. To tackle these challenges this work proposes the Distributed Evolutionary Hyperparameter Optimization (DEHO) for the Weighted Multivariate Fuzzy Time Series method (WMVFTS), a simple and non-parametric forecasting method with high scalability and accuracy, comprising a sequential training and forecasting procedure and a MapReduce extension for distributed processing. The proposed methods were evaluated using a cluster with commodity hardware and two big time series, showing increasing speed up for training and test times as new CPU cores are added to cluster. Then the DEHO method was executed in the computational cluster, achieving fast convergence and feasible processing time and generating highly accurate WMVFTS models.

Detection and attribution of abrupt shift in minor periods in human-impacted streamflow

Understanding the long-term variability of streamflow and its response to human activities in water-limited areas is essential for socio-hydrologic models’ development. In this study, a framework for the detection and attribution of abrupt shift of minor periods in human-impacted streamflow is proposed. First, the most significant abrupt shift in human-impacted streamflow is detected using the Pettitt test and verified based on different statistical characteristics of streamflow series (trend, periodicity, and different quantiles) and main physical causes (main reservoirs operations). According to the breakpoint, the study period was divided into approximately natural sub-period and human-impacted sub-period. Interestingly, we found the “missing” of minor (2–4-year timescale) periods of the runoff records after abrupt shift points in the study cases. To investigate its mechanisms, we proposed an Improved Multivariate Fuzzy Mean Generating Function (IMFMGF) model to simulate the natural runoff in the human-impacted period and decomposed the observed runoff into natural runoff component and human-impacted changing runoff component. Then, the periodicity of these two components was compared based on Morlet wavelet analysis and Ensemble Empirical Mode Decomposition (EEMD). Results showed that the minor periods’ wave crests and troughs of the above two components had excellent negative correspondence. The candidate mechanism is that the offsetting effects (i.e., the regular anthropogenic withdrawal or intake of water.) resulted in the disappearance of minor periods of the human-impacted observed, which can give more certain inputs into the prediction of non-stationary streamflow series.

Information Systems of Forecasting Incidence Rates of Dengue Fever Disease Using Multivariate Fuzzy Time Series

Demak Regency is one of the regions in Central Java Province with a low incidence of Dengue Fever compared to other cities and districts. Even so, DHF control needs to be done to minimize the occurrence of dengue fever, because DHF is a fairly dangerous disease. One form of controlling the number of DHF events that is widely used is using forecasting models, one of them is using Fuzzy Time Series. The Multivariate Fuzzy Time Series (MFTS) model is a development of the Fuzzy Time Series model that can be used to forecast using time series data by using more than one variable for forecasting, compared to the Fuzzy Time Series method that usually using only one variable. Based on the research results obtained, the MFTS model has a fairly accurate MAPE value, wherein the best MAPE was at 3 years scenario with MAPE 10,728%.

A Generalized Multivariate Approach for Possibilistic Fuzzy C-Means Clustering

Fuzzy c-Means (FCM) and Possibilistic c-Means (PCM) are the most popular algorithms of the fuzzy and possibilistic clustering approaches, respectively. A hybridization of these methods, called Possibilistic Fuzzy c-Means (PFCM), solves noise sensitivity defect of FCM and overcomes the coincident clusters problem of PCM. Although PFCM have shown good performance in cluster detection, it does not consider that different variables can produce different membership and possibility degrees and this can improve the clustering quality as it has been performed with the Multivariate Fuzzy c-Means (MFCM). Here, this work presents a generalized multivariate approach for possibilistic fuzzy c-means clustering. This approach gives a general form for the clustering criterion of the possibilistic fuzzy clustering with membership and possibility degrees different by cluster and variable and a weighted squared Euclidean distance in order to take into account the shape of clusters. Six multivariate clustering models (special cases) can be derivative from this general form and their properties are presented. Experiments with real and synthetic data sets validate the usefulness of the approach introduced in this paper using the special cases.

Fault diagnosis approach of rolling bearing based on NA‐MEMD and FRCMAC

This paper proposed a new method of fault diagnosis based on Noise Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) and Fuzzy Recurrent Cerebellar Model Articulation Controller (FRCMAC) Neural Networks. Aiming at the problem that during the use of the NA-MEMD method, the white noise amplitude parameter needs to be selected by artificial experience, a method of using Genetic Algorithm (GA) to optimize its auxiliary white noise parameters is proposed, which facilitates the use of NA-MEMD. We proposed a novel FRCMAC structure which improved Learning efficiency and dynamic response speed than traditional CMAC structure. First, the GA-NA-MEMD method is applied to process the vibration signals of rolling bearings, and the signals are decomposed into a group of Intrinsic Mode Functions (IMFs). Then use energy moments of IMFs as fault feature vectors to train FRCMAC neural network, a neural network structure suitable for rolling bearing fault diagnosis is obtained. Finally, the data from bearing data center of Case Western Reserve University is used to prove that the fault diagnosis method proposed in this paper is superior to other methods in diagnosis time and precision, which can meet the training requirements more quickly with limited training samples and fault diagnosis results more accurate.

A Multivariate Fuzzy Time Series Resource Forecast Model for Clouds using LSTM and Data Correlation Analysis

Today, almost all clouds only offer auto-scaling functions using resource usage thresholds, which are defined by users. Meanwhile, applying prediction-based auto-scaling functions to clouds still faces a problem of inaccurate forecast during operation in practice even though the functions only deal with univariate monitoring data. Up until now, there are still very few efforts to simultaneously process multiple metrics to predict resource utilization. The motivation for this multivariate processing is that there could be some correlations among metrics and they have to be examined in order to increase the model applicability in fact. In this paper, we built a novel forecast model for cloud proactive auto-scaling systems with combining several mechanisms. For preprocessing data phase, to reduce the fluctuation of monitoring data, we exploit fuzzification technique. We evaluate the correlations between different metrics to select suitable data types as inputs for the prediction model. In addition, long-short term memory (LSTM) neural network is employed to predict the resource consumption with multivariate time series data at the same time. Our model thus is called multivariate fuzzy LSTM (MF-LSTM). The proposed system is tested with Google trace data to prove its efficiency and feasibility when applying to clouds.

Multivariate fuzzy transform of complex-valued functions determined by monomial basis

In this paper, we introduce the multivariate fuzzy transform of higher degree of complex-valued functions. Apart from the orthogonal bases of multivariate complex polynomials of weighted Hilbert spaces that are derived by the Gram---Schmidt orthogonalization process, which can be problematic and imprecise in certain cases, we propose to compute the multivariate fuzzy transform components using a simple matrix calculus with the help of the monomial bases. By this novel approach, we derive two types of upper bound of the approximation error both of multivariate complex-valued functions and of their partial derivatives (the latter by the multivariate higher degree fuzzy transform). The results are demonstrated on examples.

An Approach to Simulate Interstitial Habitat Conditions During the Incubation Phase of Gravel‐Spawning Fish

AbstractThe incubation period represents an important development phase for successful reproduction of gravel‐spawning fish, whereby colmation processes can affect the quality of the interstitial habitat. From a sedimentary perspective, the infiltration and accumulation of fine sediments can result in a reduction of the pore space and limit the transport of oxygen‐rich surface water in the interstitials of riverbeds. From a biogeochemical perspective, the increased surface area for microbial growth can lead to an increase of respiration rates, which additionally limits the oxygen supply. The assessment and prediction of such processes on interstitial habitat quality represents a challenging task given their complex dynamic interacting processes and their high spatio‐temporal variability. This study presents a new habitat‐based modelling approach, which simulates interstitial habitat suitability (IHS) to evaluate dynamically the quality of interstitial habitat conditions during incubation. For this purpose, three key parameters (hydraulic conductivity, interstitial temperature and hyporheic respiration) are linked to the habitat requirements of different developmental stages during the incubation period (egg, hatching, larvae) via a multivariate fuzzy approach. The proposed modelling concept has been developed on the River Spoel in Switzerland, whereby results of a numerical 3D sediment transport model, together with supplementary measurements, deliver the spatio‐temporal variations of the required input data. The fuzzy approach provides results in form of maps and time series of IHS values to allow for an identification of abiotic bottlenecks during the incubation period. Hence, this approach represents a significant contribution for the restoration of reproduction areas of gravel‐spawning fish. Copyright © 2016 John Wiley & Sons, Ltd.

Multivariate Fuzzy C-Means algorithms with weighting

With the growing interest in automatic understanding, processing and summarization of data, several application domains, such as pattern recognition, machine learning and computational biology, have been making use of clustering algorithms. In the fuzzy clustering approach, Fuzzy C-Means (FCM) is the best-known method. Although FCM has performed well in cluster detection, membership values for each element assigned to each of the clusters cannot indicate how well the individuals are clustered in relation to each variable. To deal with this problem, a multivariate version of fuzzy c-means algorithm has been proposed. This proposition does not consider that there is a different relevant weight associated with each variable and that it may also be different from one cluster to another. Here, we propose two multivariate fuzzy c-means algorithms with weighting. Weights aim to represent how important each different variable is for each cluster and to improve the clustering quality. Furthermore, we propose tools based on suitable dispersion measures for interpretation of the fuzzy partition and fuzzy clusters obtained by multivariate fuzzy c-means methods. These tools allow the measurement of the overall quality, homogeneity of clusters and the role of different variables in the cluster formation process. To evaluate the performance of the proposed algorithms against other methods established by the clustering literature, experiments are performed with synthetic and UCI repository data sets, showing the usefulness of the algorithms with weighting.

PERFORMANCE EVALUATION OF DISTANCE MEASURES IN PROPOSED FUZZY TEXTURE MODEL FOR LAND COVER CLASSIFICATION OF REMOTELY SENSED IMAGE

Land cover classification is a vital application area in satellite image processing domain. Texture is a useful feature in land cover classification. The classification accuracy obtained always depends on the effectiveness of the texture model, distance measure and classification algorithm used. In this work, texture features are extracted using the proposed multivariate descriptor, MFTM/MVAR that uses Multivariate Fuzzy Texture Model (MFTM) supplemented with Multivariate Variance (MVAR). The K_Nearest Neighbour (KNN) algorithm is used for classification due to its simplicity coupled with efficiency. The distance measures such as log likelihood, Manhattan, Chi squared, Kullback Leibler and Bhattacharyya were used and the experiments were conducted on IRS P6 LISS-IV data. The classified images were evaluated based on error matrix, classification accuracy and Kappa statistics. From the experiments, it is found that log likelihood distance with MFTM/MVAR descriptor and KNN classifier gives 95.29% classification accuracy.

Higher Order Multivariate Fuzzy Approximation by basic Neural Network Operators

Higher Order Multivariate Fuzzy Approximation by basic Neural Network Operators

A weighted multivariate Fuzzy C-Means method in interval-valued scientific production data

Clustering is the process of organizing objects into groups whose members are similar in some way. Most of the clustering methods involve numeric data only. However, this representation may not be adequate to model complex information which may be: histogram, distributions, intervals. To deal with these types of data, Symbolic Data Analysis (SDA) was developed. In multivariate data analysis, it is common some variables be more or less relevant than others and less relevant variables can mask the cluster structure. This work proposes a clustering method based on fuzzy approach that produces weighted multivariate memberships for interval-valued data. These memberships can change at each iteration of the algorithm and they are different from one variable to another and from one cluster to another. Furthermore, there is a different relevance weight associated to each variable that may also be different from one cluster to another. The advantage of this method is that it is robust to ambiguous cluster membership assignment since weights represent how important the different variables are to the clusters. Experiments are performed with synthetic data sets to compare the performance of the proposed method against other methods already established by the clustering literature. Also, an application with interval-valued scientific production data is presented in this work. Clustering quality results have shown that the proposed method offers higher accuracy when variables have different variabilities.

High Degree Multivariate Fuzzy Approximation by Quasi-Interpolation Neural Network Operators

High Degree Multivariate Fuzzy Approximation by Quasi-Interpolation Neural Network Operators