## What is/are Fuzzy C?

Fuzzy C - The results of clustering of the proposed method are the same as those of the Fuzzy C-Means algorithm and the hierarchical clustering with ward linkage, where the clustering results produced by the AFS hierarchical clustering exhibit well-articulated semantics at each level of the hierarchy.^{[1]}The two learning strategies are summarized: 1) R-FRBFNN designed via support vector (SV)-based fuzzy C-means (FCM) clustering and softmax-based iterative reweighted least square (IRLS), which concentrate on improving the classification performance of R-FRBFNN; and 2) R-FRBFNN designed via SV-based FCM and softmax-based iterative quadratic programming (IQP), which focus on improving the robust abilities of the R-FRBFNN and reducing the effects of noise and outliers.

^{[2]}Fuzzy control is realized by designing fuzzy rules, and finally through comparison The Matlab simulation renderings of traditional PID controller and fuzzy adaptive PID controller show that the robustness and accuracy of fuzzy adaptive PID controller are better.

^{[3]}To this end, a teaching quality evaluation program based on the largest tree of fuzzy clustering is proposed.

^{[4]}Fuzzy C-means clustering was applied to analyze DNS traffic and to distinguish between human- and machine generated traffic.

^{[5]}Then the fuzzy control technology is proposed to adjust the high-speed motor of the hybrid turbocharging system.

^{[6]}Therefore, an improved IVAEGAN-based fuzzy clustering algorithm for incomplete data (IVAEGAN-FCM) is proposed based on the Internet of Things, which can better extract the hidden features and data distribution in the data.

^{[7]}In this paper, a novel locality preserving based fuzzy C-means (LPFCM) clustering method and its optimization are presented.

^{[8]}More importantly, a novel topic-detecting algorithm based on the deep learning and clustering techniques, namely deep autoencoders-based fuzzy C-means (DFCM), is introduced for analyzing the research topic trend.

^{[9]}After the experimental tests, a database was set up to develop the neurofuzzy controller.

^{[10]}An attempt was made to analyze the effectiveness of a fuzzy controller versus a conventional PID controller for an ammonia synthesis tower temperature control system, and the results were compared.

^{[11]}Despite this seeming clarity, it is in fact a fuzzy concept, insofar as the boundaries of its application shift significantly from one context to another.

^{[12]}Using analytic hierarchy process (AHP), expert scoring method, and fuzzy comprehensive evaluation method, this paper establishes a personal credit risk evaluation model of P2P online lending based on AHP method.

^{[13]}The fuzzy consolidator indicated that the region's network condition index is 63.

^{[14]}The Type2-PCM algorithm can solve the problems encountered by fuzzy c-means algorithm (FCM), Gustafson-Kessel algorithm (G-K), possibilistic c-means algorithm (PCM) and NPCM (sensitivity to noise or aberrant points and local minimal sensitivity).

^{[15]}Initially, missing values in the dataset have been imputed with the Fuzzy C-Means Rough Parameter (FCMRP) algorithm which handles the imprecision in datasets with the exploit of fuzzy and rough sets while preserving crucial information.

^{[16]}A comprehensive assessment of the key factors that affect the preference and choice of a driver for a parking space is established by the fuzzy comprehensive method.

^{[17]}We avoided this approach in this work and valued the European type exchange option using the Liu process, a Brownian motion’s fuzzy counterpart.

^{[18]}After clustering the data with the fuzzy c-means algorithm, the overall experimental data is divided into several local linear sub-models, and the model coefficients of the local linear model are obtained by partial least square regression.

^{[19]}Fuzzy cognitive maps (FCMs) are widely used fuzzy modeling tools for handling causal interdependencies in complex systems.

^{[20]}Although some researches have been devoted to weighting the base-clustering, fuzzy cluster level weighting has been ignored, more specifically, they did not pay attention to the role of cluster reliability in the fuzzy clustering ensemble.

^{[21]}This membership score calculation is based on existing soft clustering algorithms such as Fuzzy C-Means (FCM) and Gaussian Mixture Models (GMM).

^{[22]}The proposed model integrates adaptive Otsu's Threshold and Segmentation using FUZZY C-MEANS clustering for automated detection of hard yellow spots.

^{[23]}Then, the calculation process for each index weight and vulnerability index was proposed based on AHP-fuzzy comprehensive assessment methodology.

^{[24]}Fuzzy C-mean (FCM) is an algorithm for data segmentation and classification, robust and very popular within the scientific community.

^{[25]}We use expert scoring method to evaluate the membership degree of different indicators, and use Matlab R2019b statistical processing and analysis, combined with the fuzzy comprehensive evaluation model to evaluate the overall performance evaluation level of our hospital, the final score is 84.

^{[26]}The research aims to evaluate the fuzzy cluster analysis, which is a special case of cluster analysis, as well as to compare the two methods— classical and fuzzy cluster analysis.

^{[27]}The developed multi-tool approach combines, in a stepwise methodology, material flow analysis, fuzzy cognitive mapping, structural analysis, and system dynamics, to model and qualify the impact of potential and promising CE strategies.

^{[28]}In this paper, a fuzzy method, such as Fuzzy C-Means (FCM) clustering, has been used, for the very first time, to support the identification of matrices for error mitigation in quantum measurement.

^{[29]}The article mainly is aimed to analyze the process of risk-management of the innovation projects in the form of public-private partnership, to describe a methodologies of Failure mode, effects and criticality analysis and Fuzzy comprehensive evaluation model, to use above mentioned models in the evaluation of the stability risk of public-private partnership innovation projects.

^{[30]}Experimental results support the efficacy of fuzzy combination of CNNs to adaptively generate final decision score based upon confidence of each information source.

^{[31]}It has found application in fuzzy coding theory, fuzzy nite state machines and fuzzy languages.

^{[32]}This article presents a novel methodology for exact convex rewriting of nonlinear systems that generalizes the well-known sector nonlinearity approach; it allows improving the capabilities of those methodologies based on polytopes and the direct Lyapunov method, which are still an active research area of fuzzy control systems.

^{[33]}Genetic algorithm and fuzzy clustering algorithm are applied in the method.

^{[34]}In order to further develop and utilize the idle house site in rural areas, the research takes Yunnan Province as the research target, and analytic hierarchy process is used to determine the index weight, the fuzzy comprehensive evaluation method is used to carry out research on the comprehensive benefit evaluation based on idle house site development and utilization from three aspects of economic benefits, social benefits and ecological benefits.

^{[35]}The conversion system is controlled by the means of rules generated in fuzzy controller.

^{[36]}Public interest as the main content and purpose of planning is a fuzzy concept in planning literature.

^{[37]}This paper proposes a method of conflict analysis using image processing technique and fuzzy comprehensive evaluation.

^{[38]}The status information data is analyzed through the monitoring model of over-limit, synchronization, mutation and trend warning, and the status of switch is quantitatively evaluated by the fuzzy comprehensive evaluation algorithm.

^{[39]}The fuzzy control systems are robust to the errors of identification of the machine parameters and to the effect of the disturbing load torque.

^{[40]}Furthermore, the single-input structure of the fuzzy control allows for fast computation with the help of the signed distance method, which avoids using lengthy look-up tables.

^{[41]}In this paper, we propose an Energy efficient Hierarchical Clustering and Routing using Fuzzy C-Means (EHCR-FCM) which works on three-layer structure, and depends upon the centroid of the clusters and grids, relative Euclidean distances and residual energy of the nodes.

^{[42]}An online evaluation method of coal mine comprehensive level based on Fuzzy Comprehensive Evaluation method (FCE) is proposed.

^{[43]}Meanwhile, the fuzzy C‐means clustering algorithm is sensitive to noisy points and has low convergence speed.

^{[44]}Grouping over keypoints is performed using Fuzzy C-Means (FCM) clustering.

^{[45]}The aim of the research is to develop and implement software for fuzzy cognitive modeling of the level of food security in the context of import substitution, taking into account food exports.

^{[46]}In persons with a history of opioid dependence, signs of neurodegenerative changes in the cerebellar cortex were noted: deformation of the shape of Purkinje cells, morphological transformation of nuclei from karyopyknosis to karyorrhexis, and the appearance of fuzzy cell boundaries.

^{[47]}Then, fuzzy clustering is used to locate the position of the endmember quickly and accurately.

^{[48]}The first stage of CAD includes preprocessing, Fuzzy c means based segmentation applied to a localized area.

^{[49]}In each control cycle, the dynamic resistance change rate and the instantaneous maximum welding power are used as the inputs of the fuzzy controller.

^{[50]}

## means clustering algorithm

Here, the proposed modified fuzzy c means clustering algorithm is used for enhancing the tumor portion extraction process.^{[1]}To address these issues, a load uncertainty model is constructed by integrating the regional equivalent standard building-integrated load prediction method, the robust uncertainty set method and the fuzzy C-means clustering algorithm.

^{[2]}In this paper, a novel method is proposed, which is a time-domain identification algorithm, based on sliding window-fuzzy C-means clustering algorithm-combined with deterministic-stochastic subspace identification (SC-CDSI), to achieve online intelligent tracking and identification of modal parameters for nonlinear time-varying structures.

^{[3]}To design an efficient partial differential equation-based total variation method for denoising and possibilistic fuzzy c-means clustering algorithm for segmentation and these methods presented the more detailed information of the MRI medical images compared to traditional methods.

^{[4]}Scenario generation and reduction are achieved by Monte Carlo simulation and fuzzy C-means clustering algorithm.

^{[5]}Fuzzy C-means clustering algorithm (FCM) is an effective approach for clustering.

^{[6]}PCA resulting scores were introduced in the Fuzzy c-means clustering algorithm, which categorized sub-areas of the fields into two discrete zones per field.

^{[7]}Fuzzy C-means clustering algorithm is one of the typical clustering algorithms in data mining applications.

^{[8]}Based on the hourly speeding frequency and average speeding severity of each speeder, the fuzzy C-means clustering algorithm is employed to categorize taxi speeders into three cohorts: restrained speeder (RS), moderate speeder (MS), and belligerent speeder (BS).

^{[9]}The K-means and fuzzy C-means clustering algorithms were also evaluated.

^{[10]}Fuzzy C-Means clustering algorithm (FCM) is an important method to analyze MRI brain maps, but the determination of the initial clustering center will directly affect the effect of clustering.

^{[11]}In this system, the vibration and rotational speed of spindle are taken as the monitoring signals, and the feature parameters which can reflect the operating state of spindle are extracted by using the signal processing technology which combines the time domain analysis, the frequency domain analysis and the wavelet packet analysis, to establish a spindle fault identification model based on fuzzy C-means clustering algorithm, which judges the spindle state by calculating the current fault feature parameters and the membership degree of the known state in the model; finally, a set of on-line monitoring and diagnosis system software for spindle faults on automobile reducer test device is designed with LabVIEW, which is based on virtual instrument technology, as the programming tool, and the theoretical verification and the example verification are carried out in the actual automobile reducer test.

^{[12]}Aiming at the pixel misclassification and poor convergence performance of the suppressed fuzzy C-means clustering algorithm in image segmentation, an adaptive double suppressed fuzzy C-means clustering image segmentation algorithm based on regional information entropy and fuzzy partition is proposed.

^{[13]}An integrated robust Fuzzy C-Means clustering algorithm was performed on 120 combinations of five morphometric (diameter, area, height, surface volume, and slope) and two elemental features (FeO and TiO2 contents) to find the optimum combination.

^{[14]}Later, the tumor regions are segmented with the help of the optimal possibilistic fuzzy C-means clustering algorithm.

^{[15]}In CBMD the base models are selected using fuzzy c-means clustering algorithm.

^{[16]}A modified Fuzzy C-means clustering algorithm is proposed to automatically interpret the stabilization diagram, without any specifically tuned index or threshold but only with a default maximum clustering number.

^{[17]}Several methods have been proposed in the literature for regionalisation, including the method of residuals, L-moment method, and fuzzy c-means clustering algorithm.

^{[18]}This paper is a review of recent research on image fuzzy segmentation using the fuzzy c-means clustering algorithm based on a distance function constructed by applying the aggregation function on the sequence of the initial distance functions and pixel descriptors.

^{[19]}The traditional fuzzy C-means clustering algorithm (FCM) based on Euclidean distance is only applicable to clustering of spherical structures.

^{[20]}In the discriminability experiment, the kernel fuzzy C-means clustering algorithm has been employed for classifying the radar pulse modulated radiation source signals.

^{[21]}The outputs of the pre-processing phase are clustered using a fuzzy c-means clustering algorithm.

^{[22]}To evaluate the candidate predictors, we propose a kernel time-weighted fuzzy c-means clustering algorithm (KTFCM), which improves the kernel FCM algorithm (KFCM), to organize the historical samples according to their relevance to the target sample, which makes the historical samples that are closely related to the target sample have more influence on the predictors.

^{[23]}In this paper, a fault diagnosis method based on symmetric polar coordinate image and Fuzzy C-Means clustering algorithm is proposed to solve the problem that the fault signal of axial piston pump is not intuitive under the time-domain waveform diagram.

^{[24]}(2) Methods: This research applied various mathematical, statistical and artificial intelligence techniques, among which the most important are: Calinski-Harabasz index, Analytical Hierarchy Process, and Weighted Fuzzy C-means Clustering Algorithm.

^{[25]}And also to improve the LC segmentation problems a fuzzy c-means clustering algorithm (FCM) is used.

^{[26]}With the help of Raman fiber amplifiers, ultra-low loss fiber, and the optimized fuzzy C-means clustering algorithm, the results show the system can carry 10.

^{[27]}Fuzzy C-means clustering algorithm is used to classify the fault degree.

^{[28]}Finally, the mixing matrix is estimated via a fuzzy c-means clustering algorithm based on the characteristics of complex numbers.

^{[29]}Thus, to overcome the ambiguity caused by the above special effects, an enhanced fuzzy relaxation approach called fuzzy relaxation-based modified fuzzy c-means clustering algorithm is presented.

^{[30]}First, time intervals with possible arrivals on waveform recordings are identified using the fuzzy c-means clustering algorithm.

^{[31]}The fused image is segmented using Fast Fuzzy C Means Clustering Algorithm (FFCMC) and Otsu Thresholding.

^{[32]}In addition, fuzzy c-means clustering algorithm is proposed for huddling the users of the mMIMO-NOMA based communication networks.

^{[33]}Various historical feature samples which characterize different fault conditions of the protected feeder are divided into fault group and non-fault group by fuzzy c-means clustering algorithm.

^{[34]}Based on the fuzzy means clustering algorithm, a fuzzy clustering objective function including brightness, color, and distance parameters is designed, which improves the weight of the brightness value in the clustering and improves the edge fit of the segmentation of the lighting highlight area of the rendering.

^{[35]}In other words, we divide an overall input space into several subspaces by using information granulation technique (Fuzzy C-Means clustering algorithm) and determine the local decision boundaries among related subspaces.

^{[36]}The spatial distribution of the soil properties was analyzed using geostatistical analysis, a fuzzy c-means clustering algorithm, and pedodiversity analysis.

^{[37]}In the first stage, the number of formation modes is determined according to the formation characteristics and these modes are identified by the fuzzy c-means clustering algorithm.

^{[38]}The chosen features are clustered in the third stage using distance adaptive fuzzy c-means clustering algorithm (DAFCM).

^{[39]}In this paper, the fuzzy C-means clustering algorithm (FCM) is used to improve and optimize the image of breast cancer, and the experimental results are analyzed.

^{[40]}The granulation of information used in this architecture is developed using the Fuzzy C-means clustering algorithm.

^{[41]}The main article marine environment monitoring, virtual reality technology, and fuzzy C-means clustering algorithm combine to improve the efficiency of monitoring and processing power of the data information.

^{[42]}This risk factors data set is then used by fuzzy c-means clustering algorithm, to organize them into groups of different level of priorities, so as to prioritize their corresponding safety requirements.

^{[43]}The eÿcacy of the proposed technique have been analysed by comparing it with the results of tra-ditional K-Means and Fuzzy C-Means clustering algorithms.

^{[44]}In order to solve this problem, based on the engineering parameters of the remote sensor network, this paper analyzes the characteristics of the collapse stuck, and establishes the collapse stuck risks evaluation model of the fuzzy dynamic cluster algorithm to optimize Fuzzy C-means clustering algorithm.

^{[45]}On top of that, in case of the uncertain fault types, the Fuzzy C-Means clustering algorithm (FCM) optimized by Particle Swarm Optimization (PSO) was proposed to provide a priori knowledge for the model.

^{[46]}This study is aimed to group 32 selected countries according to their higher education performances using the fuzzy c-means clustering algorithm.

^{[47]}

## particle swarm optimization

This research presents the H∞ fuzzy control of an underactuated robot using particle swarm optimization (PSO) algorithms with linear matrix inequalities (LMI) stability conditions.^{[1]}The theory of fuzzy cognitive map (FCM) was designed to diagnose the fault modes of the railway turnout based on extracted feature vector, and the genetic algorithm particle swarm optimization (GAPSO) was selected to learn the weights of FCM.

^{[2]}Fuzzy clustering algorithm modelling of the data stream mining based on particle swarm optimization and GA is designed and implemented in this manuscript.

^{[3]}Fuzzy C-means clustering and particle swarm optimization are proposed to optimize the initial parameters of neural network.

^{[4]}The proposed approach initially preprocesses leaf images of plants thereafter which the diseased sections of the plant are segmented by deploying Particle Swarm Optimization (PSO)–based fuzzy c means segmentation (PSO‐FCM), Gaussian Mixture Model (GMM)–based background subtraction.

^{[5]}The performances of the proposed approach are evaluated using a set of reference images and compared to several classic clustering methods, like k-means or fuzzy c-means and other meta-heuristic approaches, such as genetic algorithms and particle swarm optimization.

^{[6]}In this paper, we propose a novel dynamically learned particle swarm optimization based neighborhood influenced fuzzy c-means (DLPSO-NIFCM) clustering (unsupervised learning model) for solving pre-treatment and post-treatment organs segmentation problems.

^{[7]}Base on the chaotic optimization theory, this study presents a chaotic particle swarm optimization (CPSO) algorithm to deal with a fuzzy clustering iterative model (CPSO-FCI) for evaluating flood hazards.

^{[8]}Then, to improve the modeling accuracy, the Fuzzy C-Means (FCM) method and the Particle Swarm Optimization (PSO) algorithm are applied to tune the weights of sub-models.

^{[9]}By applying the particle swarm optimization (PSO) to the analytic hierarchy process (AHP) and fuzzy comprehensive evaluation method, a PSO-AHP model and then a fitness function are constructed to solve and optimize the weight values in the evaluation index system, and the calculated weight values are checked by consistency checking method.

^{[10]}In the aspect of software, an adaptive fuzzy controller is designed to search the circuit signal based on the improved particle swarm optimization algorithm, and the balance control strategy of grid connected inverter circuit is set to realize the balance control of grid connected inverter circuit.

^{[11]}Focusing on the FS problem with fuzzy cost, a fuzzy multiobjective FS method with particle swarm optimization, called PSOMOFS, is studied in this article.

^{[12]}This paper attempted to connect seismic events to faults by a fuzzy particle swarm optimization algorithm, an optimized version of the fuzzy clustering approach.

^{[13]}The proposed optimization algorithm provides most promising and efficient level of image segmentation compared to Fuzzy C Means (FCM), Otsu, Particle Swarm Optimization (PSO) and Cuckoo Search (CS).

^{[14]}By introducing a Particle Swarm Optimization (PSO) initialization step and a novel dissimilarity measure metric, we present a local information kernelized fuzzy C‐means (LIKFCM) algorithm for image segmentation.

^{[15]}We use as strategy a set of clustering algorithms to group components by similarity: K-Means, K-Medoids, Fuzzy C-Means (FCM), Hierarchical, Density-Based Spatial Clustering of Applications with Noise (DBSCAN), Self-Organizing Maps (SOM), Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Differential Evolution (DE).

^{[16]}Although the successful detection of COVID-19 from lung computed tomography (CT) image mainly depends on radiologist’s experience, specialists occasionally disagree with their judgments The performance of COVID-19 detection models needs to be improved According to COVID-19 symptoms and human immune approach response, there are four types of its contagion such as asymptomatic, mild, severe, and recovered In this chapter, an automatic scoring of COVID-19 lung infection grading approach is presented The proposed approach is based on a combination of image segmentation techniques and the Particle Swarm Optimization (PSO) algorithm to access accurate evaluation for infection rate Fuzzy c-means, K-means and thresholding-based segmentation algorithms are used for isolating the chest lung from the CT images Then, PSO is used with the three segmentation algorithms for clustering the region of interest (ROI) that consists of COVID-19 infected regions in lung CT Then, scoring the infection rate for each case Finally, four infection classes related to the obtained infection COVID-19 is determined and classified © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

^{[17]}The proposed energy management combines a Gaussian-based regularized particle swarm optimization with a fuzzy clustering technique to solve the optimization problem and determine the best compromise solution according to cost-effectiveness and reliability.