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FUZZY IMPLICATIONS AND FUZZY IF-THEN MODELS
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume One, 2014
• Fuzzy Clustering: Fuzzy clustering approach (See Section 4.11) is unsuper-vised algorithm that partition data points into a given number of clusters with fuzzy boundaries. Each cluster represents a fuzzy relation, and corresponds to a rule in the rule base. The fuzzy sets in the premise part of the rules are usually identified by projecting the clusters onto the corresponding axis of the data space. This projection usually results in similar fuzzy sets, as illustrated in Figure 52. In Mamdani models, the fuzzy consequents of the rules are determined by projection too. In TS models, the consequent parameters are derived from the cluster covariance matrix or estimated using a parameters estimation technique. Different approaches to clustering can be found, such as clustering in the output space or clustering in the product pace of input and output variables. Two well known fuzzy clustering algorithms are the fuzzy c-means and the Gustafson-Kessel (GK) algorithm. The latter is especially suitable for the identification of TS fuzzy models and has been successfully applied to modeling of dynamic systems. It can be used to identify a systems mode by clustering data from system (input-output) measurements. However, before applying clustering, the number of clusters must be specified explicitly. Correct specification of the number of clusters is important. A large number results in an unnecessarily complicated rule base, while a small number may result in a poor model. Methods for finding the optimal number of clusters (rules) are already suggested.
An Integration of Blockchain and Machine Learning into the Health Care System
Published in Om Prakash Jena, Sabyasachi Pramanik, Ahmed A. Elngar, Machine Learning Adoption in Blockchain-Based Intelligent Manufacturing, 2022
Mahita Sri Arza, Sandeep Kumar Panda
The two major methods of clustering are hard clustering and soft clustering. In hard clustering, the data points are assembled into a single group. Soft clustering, on the other hand, allows data points to belong to numerous groups. There are, however, a range of different clustering techniques. The most frequently used clustering methods used in ML are as follows: Partitioning clustering—Partitioning algorithms are a type of clustering approach. It uses the K-means algorithm. The data are clustered to form “K” groups, where the value of “K” is specified by the analyst themselves. Let us consider a data set containing the parameters: customer annual income and spending. The K-means algorithm is employed in clustering the data. Figure 3.17 displays the five distinct clusters using multiple colors. These clusters can be utilized to draw certain conclusions based on the spending and annual income of the customers. Colors and labels can be changed to suit the analyst’s needs and preferences. Hierarchical clustering—The clusters created by this method form a dendrogram, which is a treelike structure based on the hierarchy. New clusters are found using the previously existing cluster. In hierarchical clustering, the number of clusters is not predefined, in contrast to the K-means clustering. Figure 3.19 depicts the visualization of the obtained clusters using hierarchical clustering. The dendrogram plot shown in Figure 3.18 determines the required number of clusters. Fuzzy clustering—Fuzzy clustering adopts soft clustering. A data point in fuzzy clustering can be assigned to more than one cluster. The fuzzy c-means method is the most widely used fuzzy clustering algorithm.Density-based clustering—It is a partitioning method first brought into use by Ester et al. [39]. It can extract clusters of various shapes and sizes from data containing noise and outliers [39]. The density-based clustering approach relies on clustering using human intuition as the primary principle.
Cluster analysis
Published in Catherine Dawson, A–Z of Digital Research Methods, 2019
Techniques and procedures that can be used for cluster analysis include (in alphabetical order): Biclustering: simultaneous clustering of the rows and columns of a data matrix. It can also be referred to as co-clustering, block clustering two-dimensional clustering or two-way clustering. See Dolnicar et al. (2012) for a discussion on this technique.Consensus clustering: a number of clusters from a dataset are examined to find a better fit. See Șenbabaoğlu et al. (2014) for an analysis and critique of this technique.Density-based spatial clustering: to filter out noise and outliers and discover clusters of arbitrary shape. See Li et al. (2015) for an example of this technique used together with mathematical morphology clustering.Fuzzy clustering: clustering data points have the potential to belong to multiple clusters (or more than one cluster). See Grekousis and Hatzichristos (2013)for an example of a study that uses this clustering technique.Graph clustering: this can include between graph (clustering a set of graphs) and within-graph (clustering the nodes/edges of a single graph). See Hussain and Asghar (2018) for a discussion on graph-based clustering methods that are combined with other clustering procedures and techniques.Hierarchical clustering: a hierarchy of clusters is built using either a bottom-up approach (agglomerative) that combines clusters, or a top-down approach (divisive) that splits clusters. It is also known as nesting clustering. See Daie and Li (2016) for an example of a study that uses matrix-based hierarchical clustering.K-means clustering: an iterative partitioning method of cluster analysis where data are clustered based on their similarity (the number of clusters is known and specified within the parameters of the clustering algorithm). See Michalopoulou and Symeonaki (2017) for an example of a study that combines k-means clustering and fuzzy c-means clustering.Model-based clustering: a method in which certain models for clusters are used and best fit between data and the models is determined (the model defines clusters). Malsiner-Walli et al. (2018) discuss this clustering technique in their paper.
Estimation of IRI from PASER using ANN based on k-means and fuzzy c-means clustering techniques: a case study
Published in International Journal of Pavement Engineering, 2022
Jalal Barzegaran, Reza Shahni Dezfoulian, Mansour Fakhri
Fuzzy c-means is a renowned fuzzy clustering algorithm. In this method, the number of clusters ‘c’ is specified and then the objective function ‘JFCM’ as shown in Equation (5) will be minimised in which uik represents the membership degree of xi data point in cluster number k and dik = states the Euclidean distance between xi and cluster centroid ‘νk’ that is calculated according to Equation (6). A constant of ‘m’ is known as a fuzzifier or fuzzy index that controls the fuzziness of acquired clusters and can be a real number equal to 1 or more. The minimisation of JFCM is performed by an alternating optimisation method and the membership degree of data points in each cluster will be updated by Equation (7). The summation of membership degrees assigned to a data point for all specified clusters must equal 1 (Sadaaki et al. 2008, Gosain and Dahiya 2016).
Daily diffuse solar radiation estimation using adaptive neuro-fuzzy inference system technique
Published in Numerical Heat Transfer, Part B: Fundamentals, 2020
The fuzzy C-means (FCM) algorithm is the most frequently used algorithm of fuzzy clustering. It detects clusters with prototypes which are points in the data space. This algorithm is derived by minimization of the criterion where is the matrix of the set X partition, whereas is the vector of centers which are to be defined as a result of the algorithm operation, The following term appearing in formula (7) permits to compute the distance vector and cluster center and is a coefficient indicating the fuzziness degree of formed clusters. When the partition becomes less and less fuzzy. When the partition becomes more and more fuzzy. Usually, the value m = 2 is chosen.
Short-term solar radiation forecasting using a new seasonal clustering technique and artificial neural network
Published in International Journal of Green Energy, 2022
Hamza Ali-Ou-Salah, Benyounes Oukarfi, Tlemcani Mouhaydine
The most well-known fuzzy clustering technique is the fuzzy c-means algorithm (FCM). In fact, this method consists of assigning each data point to multiple clusters with varying membership degrees. In Ghofrani, Ghayekhloo, and Azimi (2016), it was shown that the FCM algorithm gives better clustering results than the K-means, K-means++, K-means*, K-Medoids and SOM algorithms using different datasets such as global solar radiation, wind speed, wind direction and air temperature time series. For this reason, the FCM algorithm has been used to cluster monthly meteorological data mentioned above in order to find the seasonal repartition of solar radiation according to solar and meteorological parameters of Évora city.