Efficiency Analysis of Hybrid Fuzzy C-Means Clustering Algorithms and their Application to Compute the Severity of Disease in Plant Leaves

Data clustering has a wide range of application varying from medical image analysis, social network analysis, market segmentation, search engines, recommender systems and image processing. A clustering algorithm should be fast as well accurate. Some applications give priority to the speed of the clustering algorithms while some emphasize more on the accuracy rather than speed. A number of clustering algorithms have been proposed in the literature. Some of these include Fuzzy C-Means (FCM), Intuitionistic Fuzzy C-Means (IFCM), Rough Fuzzy C-Means (RFCM) and Rough Intuitionistic Fuzzy C-Means (RIFCM). In this paper, we compare the accuracy and execution time of the fuzzy based clustering algorithms. The clustering algorithms are applied on an image dataset and their running time as well as accuracy is compared by varying the number of clusters. Our results show that there is a clear trade-off between execution time and accuracy of these clustering algorithms. Also, we apply these algorithms on two different diseased leaf images and compute the severity of the disease of the leaves

Intuitionistic Fuzzy Possibilistic C Means Clustering Algorithms

Intuitionistic fuzzy sets (IFSs) provide mathematical framework based on fuzzy sets to describe vagueness in data. It finds interesting and promising applications in different domains. Here, we develop an intuitionistic fuzzy possibilistic C means (IFPCM) algorithm to cluster IFSs by hybridizing concepts of FPCM, IFSs, and distance measures. IFPCM resolves inherent problems encountered with information regarding membership values of objects to each cluster by generalizing membership and nonmembership with hesitancy degree. The algorithm is extended for clustering interval valued intuitionistic fuzzy sets (IVIFSs) leading to interval valued intuitionistic fuzzy possibilistic C means (IVIFPCM). The clustering algorithm has membership and nonmembership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. The experiments are performed on both real and simulated datasets. It generates valuable information and produces overlapped clusters with different membership degrees. It takes into account inherent uncertainty in information captured by IFSs. Some advantages of algorithms are simplicity, flexibility, and low computational complexity. The algorithm is evaluated through cluster validity measures. The clustering accuracy of algorithm is investigated by classification datasets with labeled patterns. The algorithm maintains appreciable performance compared to other methods in terms of pureness ratio

Properties of Bipolar Fuzzy Hypergraphs

In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy hypergraphs. We introduce the notion of $A-$ tempered bipolar fuzzy hypergraphs and present some of their properties. We also present application examples of bipolar fuzzy hypergraphs

A New Feature Selection Method based on Intuitionistic Fuzzy Entropy to Categorize Text Documents

Selection of highly discriminative feature in text document plays a major challenging role in categorization. Feature selection is an important task that involves dimensionality reduction of feature matrix, which in turn enhances the performance of categorization. This article presents a new feature selection method based on Intuitionistic Fuzzy Entropy (IFE) for Text Categorization. Firstly, Intuitionistic Fuzzy C-Means (IFCM) clustering method is employed to compute the intuitionistic membership values. The computed intuitionistic membership values are used to estimate intuitionistic fuzzy entropy via Match degree. Further, features with lower entropy values are selected to categorize the text documents. To find the efficacy of the proposed method, experiments are conducted on three standard benchmark datasets using three classifiers. F-measure is used to assess the performance of the classifiers. The proposed method shows impressive results as compared to other well known feature selection methods. Moreover, Intuitionistic Fuzzy Set (IFS) property addresses the uncertainty limitations of traditional fuzzy set

δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of Pappis (Fuzzy Sets Syst 39(1):111–115, 1991), Hong and Hwang (Fuzzy Sets Syst 66(3):383–386, 1994), Virant (2000) and Cai (IEEE Trans Fuzzy Syst 9(5):738–750, 2001) did not model the measure in the context of the intuitionistic fuzzy set but in the Zadeh’s fuzzy set instead. In this paper, we examine this problem and propose new notions of δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient’s diseases from symptoms. The idea is using δ-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets Syst 117:209–213, 2001), Samuel and Balamurugan (Appl Math Sci 6(35):1741–1746, 2012), Szmidt and Kacprzyk (2004), Zhang et al. (Procedia Eng 29:4336–4342, 2012), Hung and Yang (Pattern Recogn Lett 25:1603–1611, 2004), Wang and Xin (Pattern Recogn Lett 26:2063–2069, 2005), Vlachos and Sergiadis (Pattern Recogn Lett 28(2):197– 206, 2007), Zhang and Jiang (Inf Sci 178(6):4184–4191, 2008), Maheshwari and Srivastava (J Appl Anal Comput 6(3):772–789, 2016) and Support Vector Machine (SVM)

Spatial Condition in Intuitionistic Fuzzy C-Means Clustering for Segmentation of Teeth in Dental Panoramic Radiographs

 Dental panoramic radiographs heavily depend on the performance of the segmentation method due to the presence of unevenly illumination and low contrast of the images. Conditional Spatial Fuzzy C-mean (csFCM) Clustering have been proposed to achieve through the incorporation of the component and added in the FCM to cluster grouping. This algorithm directs with consideration conditioning variables that consider membership value. However, csFCM does not consider Intuitionistic Fuzzy Set to take final membership and final non-membership value into account, the effect does not wipe off the deviation by illumination and low contrast of the images completely for improvement to skip some scope. In this current paper, we introduced a new image segmentation method namely Conditional Spatial in Intuitionistic Fuzzy C-Means Clustering for Segmentation of Teeth in Dental Panoramic Radiographs. Our proposed method adds hesitation function aiming to settle the indication of the knowledge lack that belongs to the final membership function to get a better segmentation result. The experiment result shows this method achieves better segmentation performance with misclassification error (ME) and relative foreground area error (RAE) values are 4.77 and 4.27 respectively

Clustering stock price volatility using intuitionistic fuzzy sets

Clustering involves gathering a collection of objects into homogeneous groups or clusters, such that objects in the same cluster are more similar when compared to objects present in other groups. Clustering algorithms that generate a tree of clusters called dendrogram which can be either divisive or agglomerative. The partitional clustering gives a single partition of objects, with a predefined K number of clusters. The most popular partition clustering approaches are: k-means and fuzzy C-means (FCM). In k-means clustering, data are divided into a number of clusters where data elements belong to exactly one cluster. The k-means clustering works well when data elements are well separable. To overcome the problem of non-seprability, FCM and IFCM clustering algorithm were proposed. Here we review the use of FCM/IFCM with reference to the problem of market volatility