Intuitionistic Fuzzy C-means Algorithm Research Articles

An adaptive categorical effect size method based on intuitionistic meta fuzzy functions

There are several categorical effect size methods in the literature. It is not clear which method performs better for a given dataset and it is a challenging task to select the correct method for a given dataset. In this sense, to overcome the questions like “Which method should we choose?” and “Which categorical effect size method is more reliable for a given dataset?”, an adaptive categorical effect size method based on intuitionistic meta fuzzy functions is introduced in the paper. Thus, the main motivation of the proposed method is to obtain more accurate outcomes by combining the results of better performing methods instead of relying on only one method. In the study, the intuitionistic fuzzy c-means clustering algorithm is adapted to meta fuzzy functions by incorporating not only membership degrees but also non-membership degrees to improve the clustering accuracy of meta fuzzy functions. Meta fuzzy functions are the linear combination of seven categorical effect size methods and the weights, which are calculated from membership grades from intuitionistic fuzzy c-means algorithm. Among the functions, the one with the lowest mean absolute percentage error is selected as the best. To evaluate the performance of the proposed method, 2 × 3, 2 × 4, and 3 × 4 contingency tables were simulated. Additionally, the performance of the proposed method is also assessed by applying it to a real-time dataset. Experimental results show that the proposed method outperforms compared to the evaluated seven categorical effect size methods in terms of mean absolute percentage error. Also, the calculated effect sizes are within the range of ±10% in terms of bias. Thus, the results verified that proposed method achieves greater reliability.

IVOMFuse: An image fusion method based on infrared-to-visible object mapping

Due to the significant difference in the structure of infrared and visible images, most of the existing algorithms use globally consistent strategy, which may weaken the contrast of the target region. To solve this problem, we propose an infrared and visible image fusion method based on infrared-to-visible object mapping (IVOMFuse) First of all, we use the probability induced intuitionistic fuzzy C-means algorithm (PIIFCM) to process the infrared image, and extract the target region of the infrared image according to the image structure features. However, because of the poor contrast of the target of the visible image, it can not be segmented directly. For this reason, we map the infrared target region to the visible image, and the target region with the same coordinates of the two images can be obtained very quickly. Secondly, due to the significant differences in image structure, we set a hybrid fusion strategies for different regions. We use the fusion strategy based on the Expectation-Maximization (EM) algorithm to iterate and optimize the probability model for the target region. The fourth-order partial differential equation (FPDE) is used for the background region to decompose the source image into high-frequency texture and low-frequency approximation images respectively. Then, the principal component analysis (PCA) and the average fusion strategy are used to obtain the fused image. Finally, we evaluated our algorithm with fourteen other state-of-the-art image fusion methods on three commonly used datasets, namely TNO, CVC14, and RoadScene. Among the ten evaluation metrics, our algorithm achieved the best six times.

Probabilistic intuitionistic fuzzy c-means algorithm with spatial constraint for human brain MRI segmentation

Probabilistic intuitionistic fuzzy c-means algorithm with spatial constraint for human brain MRI segmentation

A new explainable robust high-order intuitionistic fuzzy time-series method

Fuzzy time series, based on type-1 fuzzy sets, continue to have a wide range of use in the literature. These methods use only membership values to determine the fuzzy relations. However, intuitionistic fuzzy time series models use both membership values and non-membership values. So it can be considered that the use of intuitionistic fuzzy time forecasting models will be able to increase the forecasting performance because the intuitionistic fuzzy sets have more information than fuzzy sets. Therefore, intuitionistic fuzzy time series models have started to employ for forecasting the real-life series in the fuzzy time series literature. A novel, explainable, robust high-order intuitionistic fuzzy time series forecasting method is proposed based on a newly defined model. In the proposed method, the intuitionistic fuzzy c-means algorithm is used for the fuzzification of observations, and a robust regression method employed for determining fuzzy relations. With the use of robust regression in determining the fuzzy relationships, all inputs of the proposed method can be explainable and they can be tested and commented on statistically. Applications of this study are made by using energy data of Primary Energy Consumption between the years 1965 and 2016 for 23 countries in the region of Europe-Eurasia. The forecasting performance of the proposed method is compared with the performance of some selected benchmarks, and the obtained results are discussed.

Spatial Rough Intuitionistic Fuzzy C-Means Clustering for MRI Segmentation

Medical image segmentation is the challenging problem in real-time applications due to the occurrence of noise and uncertainties between different tissues in the magnetic resonance images (MRI). To overcome the issue, spatial rough intuitionistic fuzzy C-means method has been proposed. The segmentation of MR brain image has been implemented by updating the MRI based on global spatial information of pixel with intuitionistic fuzzy c-means algorithm for segmenting cerebro spinal fluid, white matter and gray matter tissues. Intuitionistic fuzzy sets and rough sets have been used to deal with uncertainty and vagueness in medical images. Intuitionistic fuzzy sets are used for image representations by using non-membership value, hesitation along with the membership value for the MR image. The membership value and non-membership value have been obtained using fuzzy hexagonal membership and fuzzy complement function respectively. Further, roughness measures are done to determine the initial cluster centroids by considering lower and upper approximation and the fuzzy c-means clustering algorithm has been updates by the euclidean distance between the pixels based on global spatial information for segmenting MR brain image. The proposed method have been implemented and analysed with quantitative and qualitatively for the synthetic and real MR images. Experimental results exhibit a higher degree of segmentation accuracy on both synthetic and real MR images compared to existing methods and achieves better performance.

Intuitionistic Fuzzy C-Means Algorithm Based on Membership Information Transfer-Ring and Similarity Measurement.

The fuzzy C-means clustering (FCM) algorithm is used widely in medical image segmentation and suitable for segmenting brain tumors. Therefore, an intuitionistic fuzzy C-means algorithm based on membership information transferring and similarity measurements (IFCM-MS) is proposed to segment brain tumor magnetic resonance images (MRI) in this paper. The original FCM lacks spatial information, which leads to a high noise sensitivity. To address this issue, the membership information transfer model is adopted to the IFCM-MS. Specifically, neighborhood information and the similarity of adjacent iterations are incorporated into the clustering process. Besides, FCM uses simple distance measurements to calculate the membership degree, which causes an unsatisfactory result. So, a similarity measurement method is designed in the IFCM-MS to improve the membership calculation, in which gray information and distance information are fused adaptively. In addition, the complex structure of the brain results in MRIs with uncertainty boundary tissues. To overcome this problem, an intuitive fuzzy attribute is embedded into the IFCM-MS. Experiments performed on real brain tumor images demonstrate that our IFCM-MS has low noise sensitivity and high segmentation accuracy.

Intuitionistic fuzzy c-means clustering algorithm based on a novel weighted proximity measure and genetic algorithm

In the era of big data, the research on clustering technologies is a popular topic because they can discover the structure of complex data sets with minimal prior knowledge. Among the existing soft clustering technologies, as an extension of fuzzy c-means (FCM) algorithm, the intuitionistic FCM (IFCM) algorithm has been widely used due to its superiority in reducing the effects of outliers/noise and improving the clustering accuracy. In the existing IFCM algorithm, the measurement of proximity degree between a pair of objects and the determination of parameters are two critical problems, which have considerable effects on the clustering results. Therefore, we propose an improved IFCM clustering technique in this paper. Firstly, a novel weighted proximity measure, which aggregates weighted similarity and correlation measures, is proposed to evaluate not only the closeness degree but also the linear relationship between two objects. Subsequently, genetic algorithms are utilized for identifying the optimal parameters. Lastly, experiments on the proposed IFCM technique are conducted on synthetic and UCI data sets. Comparisons with other approaches in cluster evaluation indexes indicate the effectiveness and superiority of our method.

Color-Based Image Segmentation by Means of a Robust Intuitionistic Fuzzy C-means Algorithm

To yield well-suited image segmentation results, conventional clustering algorithms depend on customized hand-crafted features as well as an appropriate initialization process. This latter aspect is a mandatory pre-requisite for convergence of the algorithm, in other words, its efficiency impacts the quality of the result. In this work, we introduce an Intuitionistic Fuzzy C-Means clustering algorithm enhanced by means of Robust Statistics, which develops an outstanding image segmentation based on a basic feature such as the color information, and it requires a reduced iteration number to converge. The non-parametric Lorentzian Redescending M-estimator is used both at initialization and iterative stages of the clustering algorithm; since, it behaves such as a robust location estimator when the centroid vector is computed, and as a weighting when the membership matrix is updated. With the fusion of both techniques, we can guarantee that the introduced clustering algorithm can efficiently develop the task of segmentation of color images and pattern recognition processes. The robustness and effectiveness of this proposal is verified by experiments on the natural color images BSDS500 dataset, as well as a simulated dataset corrupted with atypical data.

Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony

Intuitionistic fuzzy sets are extended form of type 1 fuzzy sets. The modeling methods use intuitionistic fuzzy sets have second-order uncertainty approximation so these methods may have better results than methods based on type-1 fuzzy sets. Intuitionistic fuzzy sets have been used in forecasting methods and these methods are called intuitionistic fuzzy time series forecasting methods. In this study, new intuitionistic fuzzy time series definitions are made and a new forecasting method is proposed based on intuitionistic fuzzy sets. The first contribution of the paper is to make new fuzzy and intuitionistic fuzzy time series definitions. The second contribution is to make new forecasting model definitions for fuzzy and intuitionistic fuzzy time series. The last contribution is to propose a forecasting method for single-variable high-order intuitionistic fuzzy time series forecasting model. In the proposed method, fuzzification of observations is done by using intuitionistic fuzzy c-means algorithm and fuzzy relations are defined by pi-sigma artificial neural networks. Artificial bee colony algorithm is used to train Pi-Sigma artificial neural network in the proposed method. Real-world time series applications have been made for exploring performance of the proposed method.

A modified intuitionistic fuzzy c-means clustering approach to segment human brain MRI image

Fuzzy c-means (FCM) is one of the prominent method utilized for medical image segmentation. In literature intuitionistic fuzzy c-means (IFCM) is suggested which is based on intuitionistic fuzzy sets (IFSs) theory to handle uncertainty and vagueness associated with real data. The objective function of which is defined using the hesitation degree along with membership degree. However, instead of solving the objective function analytically, the approximate solution is obtained using FCM. In this paper, we have proposed a modified intuitionistic fuzzy c-means algorithm (MIFCM) and solved analytically the objective function of the MIFCM method using Lagrange method of undetermined multiplier. To incorporate hesitation degree, two parametric intuitionistic fuzzy complements namely Sugeno’s negation function and Yager’s negation function are investigated. The performance of the MIFCM method is compared with three intuitionistic fuzzy clustering methods and the FCM on two publicly available MRI dataset and a synthetic dataset. The performance measures (average segmentation accuracy, dice score, jaccard score, false negative ratio and false positive ratio) are used to compare the performance of the MIFCM method with three variants of intuitionistic fuzzy clustering methods and the FCM. Experimental results demonstrate the superior performance of the MIFCM method over others.

A hybrid metaheuristic and kernel intuitionistic fuzzy c-means algorithm for cluster analysis

Cluster analysis is a very useful data mining approach. Although many clustering algorithms have been proposed, it is very difficult to find a clustering method which is suitable for all types of datasets. This study proposes an evolutionary-based clustering algorithm which combines a metaheuristic with a kernel intuitionistic fuzzy c-means (KIFCM) algorithm. The KIFCM algorithm improves the fuzzy c-means (FCM) algorithm by employing an intuitionistic fuzzy set and a kernel function. According to previous studies, the KIFCM algorithm is a promising algorithm. However, it still has a weakness due to its high sensitivity to initial centroids. Thus, this study overcomes this problem by using a metaheuristic algorithm to improve the KIFCM result. The metaheuristic can provide better initial centroids for the KIFCM algorithm. This study applies three metaheuristics, particle swarm optimization (PSO), genetic algorithm (GA) and artificial bee colony (ABC) algorithms. Though the hybrid method is not new, this is the first paper to combine metaheuristics and KIFCM. The proposed algorithms, PSO-KIFCM, GA-KIFCM and ABC-KIFCM algorithms are evaluated using six benchmark datasets. The results are compared with some other clustering algorithms, namely K-means, FCM, Kernel fuzzy c-means (KFCM) and KIFCM algorithms. The results prove that the proposed algorithms achieve better accuracy. Furthermore, the proposed algorithms are applied to solve a case study on customer segmentation. This case study is taken from franchise stores selling women's clothing in Taiwan. For this case study, the proposed algorithms also exhibit better cluster construction than other tested algorithms.

Intuitionistic fuzzy C-means clustering algorithms

Intuitionistic fuzzy sets (IESs) are useful means to describe and deal with vague and uncertain data. An intuitionistic fuzzy C-means algorithm to cluster IESs is developed. In each stage of the intuitionistic fuzzy C-means method the seeds are modified, and for each IFS a membership degree to each of the clusters is estimated. In the end of the algorithm, all the given IFSs are clustered according to the estimated membership degrees. Furthermore, the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets (IVIFSs). Finally, the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets.