FRFCM clustering segmentation method for medical MR image feature diagnosis

Abstract

Medical image recognition is affected by characteristics such as blur and noise, which cause medical image features that cannot be effectively identified and directly affects clinical diagnostics. In order to improve the diagnostic effect of medical MR image features, based on the FRFCM clustering segmentation method, this study combines the medical MR image feature reality, collects data for traditional clustering method analysis, and sorts out the shortcomings of traditional clustering methods. Simultaneously, this study improves the traditional clustering method by combining medical image feature diagnosis requirements. In addition, this study carried out image data processing through simulation, and designed comparative experiments to analyze the performance of the algorithm. The research shows that the FRFCM combined with the intuitionistic fuzzy set proposed in this paper has greatly improved the noise immunity and segmentation performance compared with the FCM based fuzzy set.

Keywords

FRFCM clustering feature extraction image segmentation medical diagnosis

1 Introduction

The efficiency of clinical diagnosis and treatment depends to a large extent on the quality and resolution of medical images. The reason is that medical images can describe detailed information such as human organs and organizational structures. In medical images, there is a lot of content. Among them, some areas are referred to as regions of interest, which refer to areas of the target observations in the image that provide evidence for clinical diagnosis. Similarly, some areas are referred to as areas of no interest, which are areas of the surrounding environment that are not of concern. In order to accurately identify the region of interest and minimize the interference of ROU on ROI during identification and analysis, these regions must be accurately segmented to perform effective analysis and calculation of the region of interest, and to understand and diagnose pathological, physiological, and physical information [1].

A variety of medical image imaging techniques have their own advantages and disadvantages, which makes the entire image analysis process very inefficient, because it is impossible to form an optimal algorithm while processing all the pictures. Since medical images contain a large amount of fuzzy information, it is inevitable to use fuzzy sets to process medical images. The medical image is regarded as a blurred image, and the use of the fuzzy technology for image processing has gradually developed in recent decades [2].

One of the most popular medical image segmentation algorithms is the Fuzzy Mean Clustering Method (FCM). By the previous explanation, the uncertainty in the image makes it impossible to know the exact gray value of each pixel, and the FCM assigns a membership value to the extent to which each pixel belongs to each part of the image. Because it is an unsupervised method, it can be used very effectively for medical imaging by non-professional medical people [3].

Through the above analysis, the current image clustering segmentation method has been applied in medical image analysis, and many experts and scholars have taken image segmentation as an important direction of medical development. However, in the actual situation segmentation process, the medical image cannot avoid the characteristics of blur and noise, which leads to the medical image features cannot be effectively recognized. Based on this, based on the FRFCM clustering segmentation method, this study applies it to MR image feature diagnosis, and strives to improve the medical image-assisted diagnosis.

2 Related work

Over the years, scholars have studied the FCM algorithm in depth and used it to analyze the pathological changes of human tissues. Therefore, FCM has been used in most medical image segmentation and various applications. A typical example is the use of FCM to segment MRI chest tumor images [4]. It is also suitable for tumor PET images with typical noise and low-resolution features [5] and for the separation of blood vessels from retinal imaging [6]. In these applications, algorithms for automatically detecting white matter changes in the elderly brain using FCM [7] and regions for determining abnormal chest tissue [8] have also been proposed. In addition, a series of new algorithms proposed by FCM combined with other theoretical knowledge have also achieved great results in the application of segmentation medical images. For example, the literature [9] combines FCM and segmentation techniques to automatically determine the thalamic segmentation contours of brain MRI images, and the literature [10] combines FCM and connected element frequency histograms to detect breast microcalcifications. Moreover, the literature [11] combined with the Markov random field to detect brain active areas in Functional Magnetic Resonance Imaging (FMRI). In fact, the standard FCM algorithm is particularly sensitive to noise because it does not take into account spatial background information. In order to solve this problem, scholars have carried out a lot of research and improvement [12]. Some literature uses the kernel function distance metric instead of the Euclidean distance to modify the FCM’s objective function [13], or the robust kernel function distance [14] to cluster the noise-damaged chest and brain medical image data sets.

In order to reflect the reality in more detail, the intuitionistic fuzzy set is proposed on the basis of the fuzzy set. It also cares about membership and non-affiliation, and the uncertainty information is more specific. Therefore, using the intuitionistic fuzzy set to process medical images will get better results. The clustering technique based on intuitionistic fuzzy sets has been gradually developed in the near future. Nowadays, there are few research results in the use of intuitionistic fuzzy set clustering to process medical images, and intuitionistic fuzzy information has broad application prospects in medical diagnosis and pattern recognition. Therefore, research on this type of problem is necessary. Chaira introduced an intuitionistic fuzzy algorithm that combines intuitionistic fuzzy entropy with an objective function to segment the tumor region of a CT brain scan image [15], which achieved significant results. Moreover, Chaira [16] also proposed an intuitionistic fuzzy color medical image clustering algorithm, which introduced the difference in clustering results when using different color spaces –CIELab, RGB, HSV. Iakovidis et al. [17] proposed a new similarity measure to improve the traditional clustering algorithm based on histogram cross-similarity, which includes both membership and non-affiliation information. V.P.Ananthi [18] studied clustering algorithms based on interval-valued intuitionistic fuzzy sets to analyze MR tumor images, which effectively reduced time complexity and error rate. H. Verma et al. [19] used the intuitionistic fuzzy distance measure instead of the traditional Euclidean distance and combined the spatial information from the perspective of intuitionistic fuzzy sets and proposed a new intuitionistic fuzzy clustering algorithm. The algorithm not only successfully preserves image details, but also reduces sensitivity to noise, and does not require adjustment of parameters. Moreover, it successfully divides the brain MR image into three parts: graymatter (GM), whitematter (WM), and cerebrospinal fluid (CSF). B.K.Tripathy et al. [20] proposed a rough intuitionistic fuzzy algorithm for image data and original data sets, and used the reference index to evaluate the effectiveness of the algorithm. Chaudhuri A [21] combined the fuzzy probability clustering, intuitionistic fuzzy set and intuitionistic fuzzy distance measurement to propose the intuitionistic fuzzy probability C-means clustering algorithm. Moreover, they extended the algorithm into a range-intuitive fuzzy probability C-means clustering algorithm, which has a good clustering effect on both synthetic images and real data sets.

3 Research method

In the preliminary research work of the tumor-assisted diagnosis system, it is found that the fuzzy C-means clustering method is a good clustering method. However, few scholars have applied this method to the classification and recognition process of post-medical images. In addition, many domestic scholars in the research on the classification and recognition of medical images mostly only discriminate between medical images and true and false, which is difficult to truly help doctors diagnose. For the classification and identification problem, the commonly used methods such as support vector machine are difficult to implement. Through theoretical and experimental learning, this paper uses the fuzzy C-means clustering algorithm to classify and identify medical images. Moreover, this paper directly applies the fuzzy C-means clustering algorithm to the classification and recognition application of medical images and cannot get satisfactory results. Because medical images are very complex, there are certain errors in describing images only through a set of scalar features. (1) Fuzzy C-means clustering

The classic FCM algorithm is derived from the K-means clustering algorithm. In the K-means clustering algorithm, each sample belongs to a class with a membership of either 0 or 1. Moreover, by introducing the fuzzy theory, the fuzzy membership degree is defined as the degree of membership of each sample belonging to a certain class, that is, each sample can belong to multiple types at the same time. At this time, the membership of each sample belonging to a certain class is no longer a certain 0 or 1 but may be any value within the interval.

The traditional FCM algorithm was originally proposed by Dunn in 1974. He extends the objective function of the K-means clustering algorithm into the form of the weighted sum of squares in the class and uses the weighted square of membership to represent the distance between the sample and each cluster center. The representation of the objective function is given in Equation (1). $J_{2} (U, V) = \sum_{i = 1}^{c} \sum_{k = 1}^{N} u_{ik}^{2} {∥ x_{k} - v_{i} ∥}^{2}$ (1)

Bezdek et al. improved and generalized the algorithm proposed by Dunn in 1981, and changed the weighted membership weight of Dunn to a more general fuzzy weighting, which formed a classical fuzzy C-means clustering algorithm. The central idea of the algorithm is to iteratively update the membership function u_ik and the cluster center v_i to minimize the objective function to achieve the final clustering goal. The objective function expression is shown in Equation (2). $J_{p} (U, V) = \sum_{i = 1}^{c} \sum_{k = 1}^{N} u_{ik}^{p} {∥ x_{k} - v_{i} ∥}^{2}$ (2)

Among them, c is the number of clusters, N is the number of samples, u_ikis the fuzzy membership of the k-th sample point relative to the i-th cluster center, the value range of u_ik is [0, 1], ∥x_k - v_i∥ is the Euclidean distance between the kth sample point and the cluster center of the ith cluster, and p (p > 1) is a fuzzy factor whose size determines the degree of fuzzy separation of samples in different classes. The smaller the value of p, the smaller the ambiguity of the corresponding cluster, and vice versa. However, if the value of p is too large, it will be detrimental to the declassification of the sample, which makes the cluster lose its practical significance.

Under the constraint of the objective function minimization constraint $\sum_{i = 1}^{c} u_{ik} = 1, k = 1, 2, \dots N$ , the iterative expression of the fuzzy membership degree and the cluster center obtained by the standard Lagrangian multiplier method is as follows: $u_{ik} = \frac{1}{\sum_{j = 1}^{c} {(\frac{∥ x_{k} - v_{i} ∥}{∥ x_{j} - v_{i} ∥})}^{2 / (P - 1)}}$ (3) $v_{i} = \frac{\sum_{k = 1}^{N} u_{ik}^{p} x_{k}}{\sum_{k = 1}^{N} u_{ik}^{p}}$ (4) $∥ U^{'} - U ∥ = \sum_{i = 1}^{c} \sum_{k = 1}^{N} {(u_{ik}^{'} - u_{ik})}^{2}$ (5) he algorithm iteratively updates the fuzzy membership matrix and the cluster center according to formulas (3) and (4). When the difference between the two iterative fuzzy membership matrices calculated according to formula (5) is less than the specified threshold ɛ, or the maximum number of iterations is reached, the algorithm stops iterating. Based on the fuzzy membership matrix U = [u_ik] at this time, the cluster to which each sample point belongs is calculated.

Due to its simple and efficient clustering characteristics, FCM algorithm is widely used in data analysis, pattern recognition, image segmentation and other fields. In recent years, in the field of medical imaging, the FCM algorithm has developed rapidly in the module of medical image segmentation. However, traditional algorithms have obvious shortcomings when segmenting noise images. For example, the initial values of the cluster number, initial cluster center and fuzzy factor need to be set in advance, and whether the initial parameters are appropriate directly affects the accuracy of the post-segment results. Solving these problems has become a research hotspot of scholars in recent years. Many scholars have proposed many improved image segmentation algorithms based on FCM algorithm which can obtain higher segmentation precision by introducing spatial information.

(2) Traditional semi-supervised fuzzy C-means clustering algorithm

Moreover, the focus of research in the field of machine learning and pattern recognition has gradually shifted to semi-supervised learning. Semi-supervised learning combines the advantages of supervised learning and unsupervised learning, and its starting point is to study how to use a small number of labeled samples and a large number of unlabeled samples for training and classification. Then, by using a small amount of supervised information of the labeled sample points, the clustering of a large number of unmarked sample points is assisted and guided to guide the entire clustering process. In addition, semi-supervised learning has important practical significance in reducing the cost of tagging information and improving the performance of learning machines.

In 1997, Witold Pedrycz introduced the classification information of a small number of labeled samples as supervised information into the optimization process of the objective function by studying and analyzing the working principle and limitations of the traditional FCM algorithm. At the same time, the classification process of the sampled samples guides the optimization process of the objective function, so as to achieve the purpose of clustering and propose a semi-supervised FCM clustering algorithm. The expression of its objective function is as follows: $J = \sum_{i = 1}^{c} \sum_{k = 1}^{N} u_{ik}^{P} d_{ik}^{2} + α \sum_{i = 1}^{c} \sum_{k = 1}^{N} {(u_{ik} - f_{ik} b_{k})}^{p} d_{ik}^{2}$ (6)

Among them, c is the number of clusters, N is the total number of samples, u_ik is the fuzzy membership of the k-th sample point belonging to the i-th class, the range of u_ik is [0, 1], d_ik is the Euclidean distance between the kth sample point and the cluster center of the ith cluster, (α ⩾ 0) is a balance factor used to balance the unsupervised and supervised components of the objective function. The value α of is N/M and M is the number of labeled samples. b_k = b [k] k = 1, 2, ⋯ , Nis a Boolean marker vector with a labeled sample value of 1, and a non-marked sample value of 0, F = [f_ik] i = 1, 2, ⋯ , c, k = 1, 2, ⋯ , N is the membership matrix of the labeled sample, that is, f_ik represents the membership degree of the label sample k belonging to the i-th cluster, and p is the blur factor, which is an empirical value and has a value of 2.

Similar to the classical FCM algorithm, under the constraint of the objective function minimization constraint $\sum_{i}^{c} u_{ik} = 1, k = 1, 2, \dots N$ , the iterative expression formula of the fuzzy membership u_ik and the cluster center v_i solved by the standard Lagrange multiplier method is as follows. $u_{ik} = \frac{1}{1 + α} [\frac{1 + α (1 - b_{k} \sum_{i = 1}^{c} f_{ik})}{\sum_{j = 1}^{c} \frac{d_{ik}^{2}}{d_{jk}^{2}}} + α f_{ik} b_{k}]$ (7) $v_{i} = \frac{\sum_{k = 1}^{n} u_{ik}^{2} x_{k}}{\sum_{k = 1}^{n} u_{ik}^{2}}$ (8) $∥ U^{'} - U ∥ = \sum_{i = 1}^{c} \sum_{k = 1}^{N} {(u_{ik}^{'} - u_{ik})}^{2}$ (9)

The algorithm iteratively updates the fuzzy membership matrix and the cluster center according to formulas (7) and (8). When the difference between the two iterative fuzzy membership matrices calculated according to formula (9) is less than the specified threshold, or the maximum number of iterations is reached, the algorithm stops iterating. Based on the fuzzy membership matrix U = [u_ik] at this time, the cluster to which each sample point belongs is calculated.

This paper makes an improvement on the objective function, and its expression formula is shown in formula (10):

$\begin{matrix} J & = \sum_{i = 1}^{c} \sum_{k = 1}^{N} u_{ik}^{P} d_{ik}^{2} + α \sum_{i = 1}^{c} \sum_{k = 1}^{N} {(u_{ik} - f_{ik} b_{k})}^{p} d_{ik}^{2} \\ + β \sum_{i = 1}^{c} \sum_{k = 1}^{N} {(u_{ik} - \bar{b_{k}} f_{ref} ik)}^{p} d_{ik}^{2} \end{matrix}$ (10)

Through experimental verification, it is found that if the β is too large, it will affect the clustering process of the labeled samples, but the classification accuracy will be reduced. However, if the value of βis too small, the algorithm degenerates to the traditional semi-supervised FCM method. Through many experiments, the value of β is α/ - 2. Both $\bar{b_{k}}$ and b_k are Boolean mark vectors, but the values of the two are opposite, the sample value of the mark is 0, and the value of the unmarked sample is 1. The expression of f_ref is shown in formula (11), that is, the mean value of the membership of the labeled sample in the range of the specified threshold ɛ₂ in the labeled sample and the unlabeled sample is taken as the reference membership of the unlabeled sample. $f_{ref} = \frac{1}{N} \sum_{\underset{d_{jk} ⩽ ɛ_{2}}{x_{j}} \in N_{k}} f_{ij}$ (11)

Similarly, the Lagrange multiplier method is used to solve the objective function to obtain the iterative formula of the fuzzy membership matrix u_ik and the cluster center v_ias follows: $u_{ik} = \frac{1}{1 + α + β} [\frac{1 + α (1 - b_{k} \sum_{m = 1}^{c} f_{mk}) + β (1 - \bar{b_{k}} \sum_{m = 1}^{c} f_{ref} ik)}{\sum_{m = 1}^{c} \frac{d_{ik}^{2}}{d_{mk}^{2}}} + α b_{k} f_{ik} + β \bar{b_{k}} f_{ref} ik]$ (12)

$v_{i} = \frac{\sum_{k = 1}^{N} (u_{ik}^{2} + α (u_{ik} - b_{k} f_{ik}^{2}) + β {(u_{ik} - \bar{b_{k}} f_{ref} ik)}^{2}) x_{k}}{\sum_{k = 1}^{N} (u_{ik}^{2} + α {(u_{ik} - b_{k} f_{ik})}^{2} + β {(u_{ik} - \bar{b_{k}} f_{ref} ik)}^{2})}$ (13)

Similar to the clustering process of the traditional semi-supervised FCM clustering algorithm, the algorithm iteratively updates the fuzzy membership matrix and cluster center according to formulas (12) and (13). When the difference between the two iterative membership matrices calculated according to formula (9) is less than the specified threshold or the algorithm reaches the maximum number of iterations, the algorithm stops iterating. According to the fuzzy membership matrix U = [u_ik] at this time, the category to which each sample point belongs is calculated, that is, the clustering process of the sample is completed.

In summary, the flow of the algorithm in this paper is as follows:

Input: a set of medical images extracted by an image segmentation algorithm;

Output: classification result of medical image;

Initialization: A matrix of features of all medical images is calculated. Moreover, normalization is performed to determine the number of cluster centers c, the maximum number of iterations L_max, the algorithm termination threshold ɛ₁, the balance parameter α, β, the blur factor p, and the distance threshold ɛ₂ of the unlabeled sample and the labeled sample.

Initializing the fuzzy membership matrix and the cluster center. Algorithm steps: First, according to formulas (12) and (13), the fuzzy membership matrix and the cluster center are updated. Thereafter, step (1) is repeated until the difference between the two iteration membership matrices is less than the specified threshold ɛ₁, or the maximum number of iterations L_maxis reached. All samples are classified according to the calculated fuzzy membership matrix U.

4 Experimental results

First, the proposed FRFCM algorithm is compared with the fast FCM algorithm. After that, the two algorithms perform clustering and Gaussian noise on the cell maps with Gaussian noise and salt and pepper noise. FRFCM and FCM can filter most of the Gaussian noise. However, FRFCM filters out noise points near the edges more thoroughly, while FCM still leaves isolated noise points near the edges. For the segmentation effect, the edge of the cell image after FRFCM segmentation is smoother, and the FCM segmentation has more edge burrs. The results are shown in Figs. 1 –6, and Figs. 1 –3 are cell images with Gaussian noise. Figures 2 –4 are cell images with salt and pepper noise.

Fig. 1

Cell image with Gaussian noise.

Fig. 2

FCM treatment effect of Gaussian noise cell image.

Fig. 3

FRFCM treatment effect of Gaussian noise cell image.

Fig. 4

Cell image with salt and pepper noise.

Fig. 5

FCM treatment effect of cell image of pepper and salt noise.

Fig. 6

FRFCM treatment effect of cell image of pepper and salt noise.

In this paper, the proposed FRFCM algorithm and FCM algorithm are used to cluster and segment the brain MRI slices with Gaussian noise, salt and pepper noise and particle noise, and analyze and compare the results. Figure 7(a) to 7(d) respectively show the original MRI slice of the brain, the Gaussian noise Fig. with a mean of 0 and a variance of 0.005, a salt and pepper noise Fig. with a noise density of 0.05, and a particle noise Fig. with a noise density of 0.06. The processing results are shown in Figs. 8 and 9.

Fig. 7

Brain MRI slices and added noise image. (a) Original brain MRI slice (b) Image with Gaussian noise (c) Image with salt and pepper noise (d) Image with particle noise..

Fig. 8

MRI image results processed by FCM.

Fig. 9

MRI image results processed by FRFCM.

5 Analysis and discussion

However, when the method is applied to the classification and recognition of medical images, the magnitude of the improvement obtained does not reach the expected target relative to the unsupervised FCM algorithm. Through continuous experimental research, it is found that the main reason is that a small number of labeled medical image samples have certain limitations on the guidance of a large number of non-marked medical image samples, and it is very difficult to obtain a large number of medical image samples marked by professional doctors in reality.

In the process of introducing semi-supervised theory into cluster analysis, this study attempts to use a small number of classification categories of labeled samples as supervision information to guide the clustering process of a large number of unlabeled sample data, in order to obtain ideal clustering results.In the process of medical classification and recognition, it is very difficult to obtain a large number of samples. In order to make full use of the doctor’s mark information on medical images, this paper introduces the mark information of some doctors as a supervision sample. At the same time, this paper calculates the reference membership degree by using the membership degree of the similarly labeled samples and uses the reference membership degree to guide the clustering process of the unlabeled samples, so that the non-marked samples can be clustered more accurately.

Therefore, it is not possible to obtain a satisfactory result by extracting a set of scalar features to describe a medical image for classification and recognition. The traditional semi-supervised FCM clustering algorithm introduces tag information to guide the tag samples to cluster faster by marking the class information of the samples, thereby guiding the entire clustering process. The traditional semi-supervised FCM clustering algorithm is applied to the classification and recognition of medical images. Moreover, the medical images of a small number of markers have certain limitations on the guidance of a large number of unlabeled medical image samples. In addition, the clustering process of the semi-supervised FCM clustering algorithm is performed by calculating the distance between the sample feature vector and the cluster center. That is, the closer the distance between two sample feature vectors, the more likely it is to be assigned to the same class. Finally, this paper introduces the professional doctor’s mark information of some images as the supervised sample and uses the membership degree of the similarly similar labeled samples to calculate a reference membership degree and uses the reference membership degree to guide the clustering process of the non-marked samples, so that the non-marked samples can be clustered more accurately.

It can be seen from Fig. 4 that for the salt and pepper noise, the FRFCM algorithm has a good ability to remove the salt and pepper noise, and the image after clustering and division basically no longer has residual noise points. However, the FCM algorithm basically cannot remove the salt and pepper noise, and the entire image is as full of noise points as the original noise image.

When segmenting a brain MRI slice containing Gaussian noise, many noise points remain in the upper part of the image after FCM processing, and the boundary of the lesion area is rough. The comparison results show that the image noise points after FRFCM processing have all been cleared, and the boundary of the lesion area is relatively smooth. For images with salt and pepper noise, the FCM processed image still contains scattered noise points, and the FRFCM segmentation image eliminates the noise effect. Moreover, FCM and FRFCM segmentation of the particle noise image can filter out the noise better, but the edge of the FRFCM segmentation is smoother.

6 Conclusion

This study introduces the medical doctor’s mark information of the medical image as the supervised sample, calculates the reference membership degree by using the membership degree of the similarly labeled sample, and uses the reference membership degree to guide the clustering process of the non-marked sample, so that non-marked samples can be clustered more accurately. In addition, in order to study the effectiveness of the image segmentation algorithm proposed in this paper, design experiments are carried out for verification analysis. First, the proposed FRFCM algorithm is compared with the fast FCM algorithm. Then, the proposed FRFCM algorithm and FCM algorithm are used to cluster and segment the brain MRI slices with Gaussian noise, salt and pepper noise and particle noise respectively, and the results are analyzed and compared.

References

, Zang

, Chai

, et al., Automatic multiorgan segmentation in CT images of the male pelvis using region-specific hierarchical appearance cluster models[J], Medical Physics 43(10) (2016), 5426–5436.

, Chen

, Shi

, et al., Automatic Liver Segmentation Based on Shape Constraints and Deformable Graph Cut in CT Images[J], IEEE transactions on Image Processing 24(12) (2015), 5315–5329.

Song

, Kang

, Zhang

, et al., Kidney segmentation in CT sequences using SKFCM and improved GrowCut algorithm[J], BMC Systems Biology 9 Suppl 5(Suppl 5) (2015), S5.

Yang-Yuan

, Cheng-Tang

, Chen-Ming

, et al., Enteroscopic Diagnosis and Management of Small Bowel Diverticular Hemorrhage: A Multicenter Report from the Taiwan Association for the Study of Small Intestinal Diseases[J], Research and Practice 2015 (2015), 1–4.

Zhou

, Ke

and Luo

, Multi-camera transfer GAN for person re-identification, J Vis Commun Image Represent 59 (2019), 393–400.

Lokesh

, Kanisha

, Nalini

, et al., Speech to speech interaction system using Multimedia Tools and Partially Observable Markov Decision Process for visually impaired students[J], Multimedia Tools and Applications 2018.

Roberto

and Toppano

, Multimedia analysis and design: a conceptual framework[J], Multimedia Tools and Applications 2019(1/4).

, Zhao

, Chen

, et al., Performance and power consumption tradeoff in multimedia cloud[J], Multimedia Tools and Applications 2018.

Bakiya

, Kamalanand

, Rajinikanth

, et al., Deep neural network assisted diagnosis of time-frequency transformed electromyograms[J], Multimedia Tools and Applications 2018.

10.

Zhou

and Tan

, Electrocardiogram soft computing using hybrid deep learning CNN-ELM, Soft Comput 86 (2020).

11.

Yen

V.T.

, Nan

W.Y.

and Van Cuong

, Recurrent fuzzy wavelet neural networks based on robust adaptive sliding mode control for industrial robot manipulators, Neural Comput & Applic 31 (2019), 6945–6958.

12.

Urtnasan

, Park

and Lee

, Automatic detection of sleep-disordered breathing events using recurrent neural networks from an electrocardiogram signal, Neural Comput & Applic 32 (2020), 4733–4742.

13.

Kaur

and Singh

, Hybrid intrusion detection and signature generation using Deep Recurrent Neural Networks, Neural Comput & Applic 32 (2020), 7859–7877.

14.

Sakar

C.O.

, Polat

S.O.

, Katircioglu

, et al., Real-time prediction of online shoppers’ purchasing intention using multilayer perceptron and LSTM recurrent neural networks, Neural Comput & Applic 31 (2019), 6893–6908.

15.

Chaira

, Intuitionistic fuzzy color clustering of human cell images on different color models[J], Journal of Intelligent & Fuzzy Systems 23(2, 3) (2012), 43–51.

16.

Chaira

, Medical image processing: Advanced fuzzy set theoretic techniques[M], CRC Press, 2015.

17.

Iakovidis

D.K.

, Georgakopoulos

S.V.

, Vasilakakis

, et al., Detecting and locating gastrointestinal anomalies using deep learning and iterative cluster unification[J], IEEE transactions on medical imaging 37(10) (2018), 2196–2210.

18.

Ananthi

V.P.

, Balasubramaniam

and Kalaiselvi

, A new fuzzy clustering algorithm for the segmentation of brain tumor[J], Soft Computing 20(12) (2016), 4859–4879.

19.

Verma

and Merigó

J.M.

, On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision-making[J], International Journal of Intelligent Systems 34(10) (2019), 2556–2583.

20.

Tripathy

B.K.

, Sooraj

T.R.

and Mohanty

R.K.

, A new approach to interval-valued fuzzy soft sets and its application in decision-making[M], Advances in Computational Intelligence. Springer, Singapore, 2017:3–10.

21.

Chaudhuri

and De

, Fuzzy support vector machine for bankruptcy prediction[J], Applied Soft Computing 11(2) (2011), 2472–2486.