As per World Health Organization report which was released in the year of 2019,Diabetes claimed the lives of approximately 1.5 million individuals globally in 2019 and around 450 million people are affected by diabete...As per World Health Organization report which was released in the year of 2019,Diabetes claimed the lives of approximately 1.5 million individuals globally in 2019 and around 450 million people are affected by diabetes all over the world.Hence it is inferred that diabetes is rampant across the world with the majority of the world population being affected by it.Among the diabetics,it can be observed that a large number of people had failed to identify their disease in the initial stage itself and hence the disease level moved from Type-1 to Type-2.To avoid this situation,we propose a new fuzzy logic based neural classifier for early detection of diabetes.A set of new neuro-fuzzy rules is introduced with time constraints that are applied for thefirst level classification.These levels are further refined by using the Fuzzy Cognitive Maps(FCM)with time intervals for making thefinal decision over the classification process.The main objective of this proposed model is to detect the diabetes level based on the time.Also,the set of neuro-fuzzy rules are used for selecting the most contributing values over the decision-making process in diabetes prediction.The proposed model proved its efficiency in performance after experiments conducted not only from the repository but also by using the standard diabetic detection models that are available in the market.展开更多
Induction motor (IM) is commonly used in various industrial applications. Reliable online IM health condition monitoring systems are critically needed in industries to improve operational accuracy and safety of the IM...Induction motor (IM) is commonly used in various industrial applications. Reliable online IM health condition monitoring systems are critically needed in industries to improve operational accuracy and safety of the IMs and the machinery. A new evolving algorithm is proposed to provide more decision-making transparency, as well as better classification and processing efficiency. The effectiveness of the developed intelligent classifier is examined by simulation and experimental tests.展开更多
This paper presents the formulation of the possibilistic Renyi entropy function from the Renyi entropy function using the framework of Hanman-Anirban entropy function. The new entropy function is used to derive the in...This paper presents the formulation of the possibilistic Renyi entropy function from the Renyi entropy function using the framework of Hanman-Anirban entropy function. The new entropy function is used to derive the information set features from keystroke dynamics for the authentication of users. A new composite fuzzy classifier is also proposed based on Mamta-Hanman entropy function and applied on the Information Set based features. A comparison of the results of the proposed approach with those of Support Vector Machine and Random Forest classifier shows that the new classifier outperforms the other two.展开更多
In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come...In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come in form of three parts, namely premise part, consequence part and aggregation part. The premise part was developed by density fuzzy c-means that helps determine the apex parameters of membership functions, while the consequence part was realized by means of two types of polynomials including linear and quadratic. L2-norm regularization that can alleviate the overfitting problem was exploited to estimate the parameters of polynomials, which constructed the aggregation part. Experimental results of several data sets demonstrate that the proposed classifiers show higher classification accuracy in comparison with some other classifiers reported in the literature.展开更多
开集分类识别是近10多年来模式识别领域研究的热点,它能够识别训练集中已知类别的测试样本,同时还能够有效“拒识”未知类别的测试样本;这些未知类别样本不包含在训练集中。现有的开集分类识别算法主要是基于Support Vector Machine(SVM...开集分类识别是近10多年来模式识别领域研究的热点,它能够识别训练集中已知类别的测试样本,同时还能够有效“拒识”未知类别的测试样本;这些未知类别样本不包含在训练集中。现有的开集分类识别算法主要是基于Support Vector Machine(SVM)和深度学习网络框架进行改进,并且主要应用在自然景物图像领域中;在光谱分析领域中还鲜有报道。将传统的闭集框架下的模糊推理分类器进行模型改进,提出了开集框架下的改进模糊推理分类器,并将其应用到木材树种近红外光谱分类识别中。首先,使用Flame-NIR近红外微型光谱仪采集木材样本横切面的近红外光谱曲线,采用Metric Learning算法进行光谱向量维度约简降维至4维(4D)。其次,改进闭集框架下的模糊推理分类器,根据模糊规则置信度和各维度隶属度概率的乘积构建Generalized Basic Probability Assignment(GBPA),再根据GBPA进行分类处理。在20个树种的具有不同的Openness指标下的近红外光谱数据集的分类识别对比实验表明,改进的开集模糊推理分类器(fuzzy reasoning classifier in an open set,FRCOS)优于现有的基于机器学习和深度学习的开集分类识别主流算法,具有较好的评价指标F-Score,Kappa系数及总体识别率。展开更多
Hazards and disasters have always negative impacts on the way of life.Landslide is an overwhelming natural as well as man-made disaster that causes loss of natural resources and human properties throughout theworld.Th...Hazards and disasters have always negative impacts on the way of life.Landslide is an overwhelming natural as well as man-made disaster that causes loss of natural resources and human properties throughout theworld.The present study aimed to assess and compare the prediction efficiency of different models in landslide susceptibility in the Kysuca river basin,Slovakia.In this regard,the fuzzy decision-making trial and evaluation laboratory combining with the analytic network process(FDEMATEL-ANP),Naïve Bayes(NB)classifier,and random forest(RF)classifier were considered.Initially,a landslide inventory map was produced with 2000 landslide and nonlandslide points by randomly dividedwith a ratio of 70%:30%for training and testing,respectively.The geospatial database for assessing the landslide susceptibility was generated with the help of 16 landslide conditioning factors by allowing for topographical,hydrological,lithological,and land cover factors.The ReliefF methodwas considered for determining the significance of selected conditioning factors and inclusion in the model building.Consequently,the landslide susceptibility maps(LSMs)were generated using the FDEMATEL-ANP,Naïve Bayes(NB)classifier,and random forest(RF)classifier models.Finally,the area under curve(AUC)and different arithmetic evaluation were used for validating and comparing the results and models.The results revealed that random forest(RF)classifier is a promising and optimum model for landslide susceptibility in the study area with a very high value of area under curve(AUC=0.954),lower value of mean absolute error(MAE=0.1238)and root mean square error(RMSE=0.2555),and higher value of Kappa index(K=0.8435)and overall accuracy(OAC=92.2%).展开更多
A new multiple models(MM) approach was proposed to model complex industrial process by using Fuzzy Support Vector Machines(F -SVMs). By applying the proposed approach to a pH neutralization titration experiment, F -SV...A new multiple models(MM) approach was proposed to model complex industrial process by using Fuzzy Support Vector Machines(F -SVMs). By applying the proposed approach to a pH neutralization titration experiment, F -SVMs MM not only provides satisfactory approximation and generalization property, but also achieves superior performance to USOCPN multiple modeling method and single modeling method based on standard SVMs.展开更多
For a semi-supervised classification system, with the increase of the training samples number, the system needs to be continually updated. As the size of samples set is increasing, many unreliable samples will also be...For a semi-supervised classification system, with the increase of the training samples number, the system needs to be continually updated. As the size of samples set is increasing, many unreliable samples will also be increased. In this paper, we use fuzzy c-means (FCM) clustering to take out some samples that are useless, and extract the intersection between the original training set and the cluster after using FCM clustering. The intersection between every class and cluster is reliable samples which we are looking for. The experiment result demonstrates that the superiority of the proposed algorithm is remarkable.展开更多
PFS-Fuzzy classification ( Lu, 1989) was used on observational data obtained during a cruise (July-August】 1987)to classify the water masses in the source area of the Tsushima Warm Current. Their mixing features were...PFS-Fuzzy classification ( Lu, 1989) was used on observational data obtained during a cruise (July-August】 1987)to classify the water masses in the source area of the Tsushima Warm Current. Their mixing features were studied by using numerical index analysis of fuzzy sets. The calculated results showed there are nine water masses belonging to three basic types.The analyses suggest that, though, in summer, the Surface Water of the Tsushima Warm Current located in a strongly mixed area is a mixture of the East China Sea Mixed Water, the Kuroshio Surface Water and the Kyushu Western Coastal Water, it originates mainly from the Kuroshio Surface Water and its deep water comes from the Kuroshio Subsurface Water. This study reveals that 1) regions such as the intensely mixed region, the frontal zone and the transition zone, Water, it originates deep water comes from water, usually have a higher fuzzy degree ; 2) water masses with higher stability and little modification have a lower fuzzy degree ; and 3)展开更多
This paper proposes an approach to detecting diseases in neem leaf that uses a Fuzzy-Higher Order Biologically Inspired Neuron Model(F-HOBINM)and adaptive neuro classifier(ANFIS).India exports USD 0.28-million worth o...This paper proposes an approach to detecting diseases in neem leaf that uses a Fuzzy-Higher Order Biologically Inspired Neuron Model(F-HOBINM)and adaptive neuro classifier(ANFIS).India exports USD 0.28-million worth of neem leaf to the UK,USA,UAE,and Europe in the form of dried leaves and powder,both of which help reduce diabetesrelated issues,cardiovascular problems,and eye disorders.Diagnosing neem leaf disease is difficult through visual interpretation,owing to similarity in their color and texture patterns.The most common diseases include bacterial blight,Colletotrichum and Alternaria leaf spot,blight,damping-off,powdery mildew,Pseudocercospora leaf spot,leaf web blight,and seedling wilt.However,traditional color and texture algorithms fail to identify leaf diseases due to irregular lumps and surfaces,and rough ridges,as the classification time involved takes as long as a week.The proposed F-HOBINM algorithm recognizes the leaf intensity through the leaky capacitor,and uses subjective intensity and physical stimulus to interpret the diagnosis.Further,the processed leaf images from the HOBINM algorithm are applied to the ANFIS classifier to identify neem leaf diseases.The experimental results show 92.18%accuracy from a database of 1,462 neem leaves.展开更多
In this paper, a hybrid Fuzzy Neural Network (FNN) system for function approximation is presented. The proposed FNN can handle numeric and fuzzy inputs simultaneously. The numeric inputs are fuzzified by input nodes u...In this paper, a hybrid Fuzzy Neural Network (FNN) system for function approximation is presented. The proposed FNN can handle numeric and fuzzy inputs simultaneously. The numeric inputs are fuzzified by input nodes upon presentation to the network while the Fuzzy rule based knowledge is translated directly into network architecture. The connections between input to hidden nodes represent rule antecedents and hidden to output nodes represent rule consequents. All the connections are represented by Gaussian fuzzy sets. The method of activation spread in the network is based on a fuzzy mutual subsethood measure. Rule (hidden) node activations are computed as a fuzzy inner product. For a given numeric o fuzzy input, numeric outputs are computed using volume based defuzzification. A supervised learning procedure based on gradient descent is employed to train the network. The model has been tested on two different approximation problems: sine-cosine function approximation and Narazaki-Ralescu function and shows its natural capability of inference, function approximation, and classification.展开更多
为了进一步提升Takagi-Sugeno-Kang(TSK)模糊分类器在不平衡数据集上的泛化能力和保持其较好的语义可解释性,受集成学习的启发,提出面向不平衡数据的深度TSK模糊分类器(A Deep TSK Fuzzy Classifier for Imbalanced Data,ID-TSK-FC).ID-...为了进一步提升Takagi-Sugeno-Kang(TSK)模糊分类器在不平衡数据集上的泛化能力和保持其较好的语义可解释性,受集成学习的启发,提出面向不平衡数据的深度TSK模糊分类器(A Deep TSK Fuzzy Classifier for Imbalanced Data,ID-TSK-FC).ID-TSK-FC主要由一个不平衡全局线性回归子分类器(Imbalanced Global Linear Regression Sub-Classifier,IGLRc)和多个不平衡TSK模糊子分类器(Imbalanced TSK Fuzzy Sub-Classifier,I-TSK-FC)组成.根据人类“从全局粗糙到局部精细”的认知行为和栈式叠加泛化原理,ID-TSK-FC首先在所有原始训练样本上训练一个IGLRc,获得全局粗糙的分类结果.然后根据IGLRc的输出,识别原始训练样本中的非线性分布训练样本.在非线性分布训练样本上,以栈式深度结构生成多个局部I-TSK-FC,获得局部精细的结果.最后,对于栈式堆叠IGLRc和所有I-TSK-FC的输出,使用基于最小距离投票原理,得到ID-TSK-FC的最终输出.实验表明,ID-TSK-FC不仅具有基于特征重要性的可解释性,而且具有至少相当的泛化性能和语义可解释性.展开更多
This paper aims to frame a new rice disease prediction model that included three major phases.Initially,median filtering(MF)is deployed during pre-processing and then‘proposed Fuzzy Means Clustering(FCM)based segment...This paper aims to frame a new rice disease prediction model that included three major phases.Initially,median filtering(MF)is deployed during pre-processing and then‘proposed Fuzzy Means Clustering(FCM)based segmentation’is done.Following that,‘Discrete Wavelet Transform(DWT),Scale-Invariant Feature Transform(SIFT)and low-level features(colour and shape),Proposed local Binary Pattern(LBP)based features’are extracted that are classified via‘MultiLayer Perceptron(MLP)and Long Short Term Memory(LSTM)’and predicted outcomes are obtained.For exact prediction,this work intends to optimise the weights of LSTM using Inertia Weighted Salp Swarm Optimisation(IW-SSO)model.Eventually,the development of IW-SSO method is established on varied metrics.展开更多
文摘As per World Health Organization report which was released in the year of 2019,Diabetes claimed the lives of approximately 1.5 million individuals globally in 2019 and around 450 million people are affected by diabetes all over the world.Hence it is inferred that diabetes is rampant across the world with the majority of the world population being affected by it.Among the diabetics,it can be observed that a large number of people had failed to identify their disease in the initial stage itself and hence the disease level moved from Type-1 to Type-2.To avoid this situation,we propose a new fuzzy logic based neural classifier for early detection of diabetes.A set of new neuro-fuzzy rules is introduced with time constraints that are applied for thefirst level classification.These levels are further refined by using the Fuzzy Cognitive Maps(FCM)with time intervals for making thefinal decision over the classification process.The main objective of this proposed model is to detect the diabetes level based on the time.Also,the set of neuro-fuzzy rules are used for selecting the most contributing values over the decision-making process in diabetes prediction.The proposed model proved its efficiency in performance after experiments conducted not only from the repository but also by using the standard diabetic detection models that are available in the market.
基金Supported by Gansu Province Natural Science Foundation(3ZS061-A25-045), and the“Qing Lan”Talent Engineering Funds of Lanazhou Jiaotong University(QL-06-19A)
文摘Induction motor (IM) is commonly used in various industrial applications. Reliable online IM health condition monitoring systems are critically needed in industries to improve operational accuracy and safety of the IMs and the machinery. A new evolving algorithm is proposed to provide more decision-making transparency, as well as better classification and processing efficiency. The effectiveness of the developed intelligent classifier is examined by simulation and experimental tests.
文摘This paper presents the formulation of the possibilistic Renyi entropy function from the Renyi entropy function using the framework of Hanman-Anirban entropy function. The new entropy function is used to derive the information set features from keystroke dynamics for the authentication of users. A new composite fuzzy classifier is also proposed based on Mamta-Hanman entropy function and applied on the Information Set based features. A comparison of the results of the proposed approach with those of Support Vector Machine and Random Forest classifier shows that the new classifier outperforms the other two.
基金This work was supported in part by the National Natural Science Foundation of China under Grant 61673295the Natural Science Foundation of Tianjin under Grant 18JCYBJC85200by the National College Students’ innovation and entrepreneurship project under Grant 201710060041.
文摘In this paper, polynomial fuzzy neural network classifiers (PFNNCs) is proposed by means of density fuzzy c-means and L2-norm regularization. The overall design of PFNNCs was realized by means of fuzzy rules that come in form of three parts, namely premise part, consequence part and aggregation part. The premise part was developed by density fuzzy c-means that helps determine the apex parameters of membership functions, while the consequence part was realized by means of two types of polynomials including linear and quadratic. L2-norm regularization that can alleviate the overfitting problem was exploited to estimate the parameters of polynomials, which constructed the aggregation part. Experimental results of several data sets demonstrate that the proposed classifiers show higher classification accuracy in comparison with some other classifiers reported in the literature.
文摘开集分类识别是近10多年来模式识别领域研究的热点,它能够识别训练集中已知类别的测试样本,同时还能够有效“拒识”未知类别的测试样本;这些未知类别样本不包含在训练集中。现有的开集分类识别算法主要是基于Support Vector Machine(SVM)和深度学习网络框架进行改进,并且主要应用在自然景物图像领域中;在光谱分析领域中还鲜有报道。将传统的闭集框架下的模糊推理分类器进行模型改进,提出了开集框架下的改进模糊推理分类器,并将其应用到木材树种近红外光谱分类识别中。首先,使用Flame-NIR近红外微型光谱仪采集木材样本横切面的近红外光谱曲线,采用Metric Learning算法进行光谱向量维度约简降维至4维(4D)。其次,改进闭集框架下的模糊推理分类器,根据模糊规则置信度和各维度隶属度概率的乘积构建Generalized Basic Probability Assignment(GBPA),再根据GBPA进行分类处理。在20个树种的具有不同的Openness指标下的近红外光谱数据集的分类识别对比实验表明,改进的开集模糊推理分类器(fuzzy reasoning classifier in an open set,FRCOS)优于现有的基于机器学习和深度学习的开集分类识别主流算法,具有较好的评价指标F-Score,Kappa系数及总体识别率。
文摘Hazards and disasters have always negative impacts on the way of life.Landslide is an overwhelming natural as well as man-made disaster that causes loss of natural resources and human properties throughout theworld.The present study aimed to assess and compare the prediction efficiency of different models in landslide susceptibility in the Kysuca river basin,Slovakia.In this regard,the fuzzy decision-making trial and evaluation laboratory combining with the analytic network process(FDEMATEL-ANP),Naïve Bayes(NB)classifier,and random forest(RF)classifier were considered.Initially,a landslide inventory map was produced with 2000 landslide and nonlandslide points by randomly dividedwith a ratio of 70%:30%for training and testing,respectively.The geospatial database for assessing the landslide susceptibility was generated with the help of 16 landslide conditioning factors by allowing for topographical,hydrological,lithological,and land cover factors.The ReliefF methodwas considered for determining the significance of selected conditioning factors and inclusion in the model building.Consequently,the landslide susceptibility maps(LSMs)were generated using the FDEMATEL-ANP,Naïve Bayes(NB)classifier,and random forest(RF)classifier models.Finally,the area under curve(AUC)and different arithmetic evaluation were used for validating and comparing the results and models.The results revealed that random forest(RF)classifier is a promising and optimum model for landslide susceptibility in the study area with a very high value of area under curve(AUC=0.954),lower value of mean absolute error(MAE=0.1238)and root mean square error(RMSE=0.2555),and higher value of Kappa index(K=0.8435)and overall accuracy(OAC=92.2%).
基金National High Technology Research andDevelopment Program of China( Project 863 G2 0 0 1AA413 13 0
文摘A new multiple models(MM) approach was proposed to model complex industrial process by using Fuzzy Support Vector Machines(F -SVMs). By applying the proposed approach to a pH neutralization titration experiment, F -SVMs MM not only provides satisfactory approximation and generalization property, but also achieves superior performance to USOCPN multiple modeling method and single modeling method based on standard SVMs.
基金supported by the National Natural Science Foundation under Grant No.61175055 and No.61105059support of research funds of Sichuan Key Laboratory of Intelligent Network Information Processing under Grant No.SGXZD1002-10Si chuan Key Technology Research and Development Program under Grant No.2012GZ0019 and No.2011FZ0051
文摘For a semi-supervised classification system, with the increase of the training samples number, the system needs to be continually updated. As the size of samples set is increasing, many unreliable samples will also be increased. In this paper, we use fuzzy c-means (FCM) clustering to take out some samples that are useless, and extract the intersection between the original training set and the cluster after using FCM clustering. The intersection between every class and cluster is reliable samples which we are looking for. The experiment result demonstrates that the superiority of the proposed algorithm is remarkable.
文摘PFS-Fuzzy classification ( Lu, 1989) was used on observational data obtained during a cruise (July-August】 1987)to classify the water masses in the source area of the Tsushima Warm Current. Their mixing features were studied by using numerical index analysis of fuzzy sets. The calculated results showed there are nine water masses belonging to three basic types.The analyses suggest that, though, in summer, the Surface Water of the Tsushima Warm Current located in a strongly mixed area is a mixture of the East China Sea Mixed Water, the Kuroshio Surface Water and the Kyushu Western Coastal Water, it originates mainly from the Kuroshio Surface Water and its deep water comes from the Kuroshio Subsurface Water. This study reveals that 1) regions such as the intensely mixed region, the frontal zone and the transition zone, Water, it originates deep water comes from water, usually have a higher fuzzy degree ; 2) water masses with higher stability and little modification have a lower fuzzy degree ; and 3)
文摘This paper proposes an approach to detecting diseases in neem leaf that uses a Fuzzy-Higher Order Biologically Inspired Neuron Model(F-HOBINM)and adaptive neuro classifier(ANFIS).India exports USD 0.28-million worth of neem leaf to the UK,USA,UAE,and Europe in the form of dried leaves and powder,both of which help reduce diabetesrelated issues,cardiovascular problems,and eye disorders.Diagnosing neem leaf disease is difficult through visual interpretation,owing to similarity in their color and texture patterns.The most common diseases include bacterial blight,Colletotrichum and Alternaria leaf spot,blight,damping-off,powdery mildew,Pseudocercospora leaf spot,leaf web blight,and seedling wilt.However,traditional color and texture algorithms fail to identify leaf diseases due to irregular lumps and surfaces,and rough ridges,as the classification time involved takes as long as a week.The proposed F-HOBINM algorithm recognizes the leaf intensity through the leaky capacitor,and uses subjective intensity and physical stimulus to interpret the diagnosis.Further,the processed leaf images from the HOBINM algorithm are applied to the ANFIS classifier to identify neem leaf diseases.The experimental results show 92.18%accuracy from a database of 1,462 neem leaves.
文摘In this paper, a hybrid Fuzzy Neural Network (FNN) system for function approximation is presented. The proposed FNN can handle numeric and fuzzy inputs simultaneously. The numeric inputs are fuzzified by input nodes upon presentation to the network while the Fuzzy rule based knowledge is translated directly into network architecture. The connections between input to hidden nodes represent rule antecedents and hidden to output nodes represent rule consequents. All the connections are represented by Gaussian fuzzy sets. The method of activation spread in the network is based on a fuzzy mutual subsethood measure. Rule (hidden) node activations are computed as a fuzzy inner product. For a given numeric o fuzzy input, numeric outputs are computed using volume based defuzzification. A supervised learning procedure based on gradient descent is employed to train the network. The model has been tested on two different approximation problems: sine-cosine function approximation and Narazaki-Ralescu function and shows its natural capability of inference, function approximation, and classification.
文摘为了进一步提升Takagi-Sugeno-Kang(TSK)模糊分类器在不平衡数据集上的泛化能力和保持其较好的语义可解释性,受集成学习的启发,提出面向不平衡数据的深度TSK模糊分类器(A Deep TSK Fuzzy Classifier for Imbalanced Data,ID-TSK-FC).ID-TSK-FC主要由一个不平衡全局线性回归子分类器(Imbalanced Global Linear Regression Sub-Classifier,IGLRc)和多个不平衡TSK模糊子分类器(Imbalanced TSK Fuzzy Sub-Classifier,I-TSK-FC)组成.根据人类“从全局粗糙到局部精细”的认知行为和栈式叠加泛化原理,ID-TSK-FC首先在所有原始训练样本上训练一个IGLRc,获得全局粗糙的分类结果.然后根据IGLRc的输出,识别原始训练样本中的非线性分布训练样本.在非线性分布训练样本上,以栈式深度结构生成多个局部I-TSK-FC,获得局部精细的结果.最后,对于栈式堆叠IGLRc和所有I-TSK-FC的输出,使用基于最小距离投票原理,得到ID-TSK-FC的最终输出.实验表明,ID-TSK-FC不仅具有基于特征重要性的可解释性,而且具有至少相当的泛化性能和语义可解释性.
文摘This paper aims to frame a new rice disease prediction model that included three major phases.Initially,median filtering(MF)is deployed during pre-processing and then‘proposed Fuzzy Means Clustering(FCM)based segmentation’is done.Following that,‘Discrete Wavelet Transform(DWT),Scale-Invariant Feature Transform(SIFT)and low-level features(colour and shape),Proposed local Binary Pattern(LBP)based features’are extracted that are classified via‘MultiLayer Perceptron(MLP)and Long Short Term Memory(LSTM)’and predicted outcomes are obtained.For exact prediction,this work intends to optimise the weights of LSTM using Inertia Weighted Salp Swarm Optimisation(IW-SSO)model.Eventually,the development of IW-SSO method is established on varied metrics.