Picture fuzzy clustering: a new computational intelligence method

Abstract

Fuzzy clustering especially fuzzy C-means (FCM) is considered as a useful tool in the processes of pattern recognition and knowledge discovery from a database; thus being applied to various crucial, socioeconomic applications. Nevertheless, the clustering quality of FCM is not high since this algorithm is deployed on the basis of the traditional fuzzy sets, which have some limitations in the membership representation, the determination of hesitancy and the vagueness of prototype parameters. Various improvement versions of FCM on some extensions of the traditional fuzzy sets have been proposed to tackle with those limitations. In this paper, we consider another improvement of FCM on the picture fuzzy sets, which is a generalization of the traditional fuzzy sets and the intuitionistic fuzzy sets, and present a novel picture fuzzy clustering algorithm, the so-called FC-PFS. A numerical example on the IRIS dataset is conducted to illustrate the activities of the proposed algorithm. The experimental results on various benchmark datasets of UCI Machine Learning Repository under different scenarios of parameters of the algorithm reveal that FC-PFS has better Communicated by V. Loia.

Some Selected Problems of Modern Soft Computing

“…Le Hoang Son et al in [11,13,14] has shown that " Picture Fuzzy Sets Theory" is a new approach to many Computational Intelligence problems . This paper reviewed some recent researches about soft computing methods on picture fuzzy sets.…”

Single-Valued Neutrosophic Clustering Algorithm Based on Tsallis Entropy Maximization

“…By replacing traditional fuzzy sets with intuitionistic fuzzy set, Chaira introduced the intuitionistic fuzzy clustering (IFC) method in [8], which integrated the intuitionistic fuzzy entropy with the objective function. Hwang and Rhee suggested deploying FCM on (interval) Type-2 fuzzy set sets in [9], which aimed to design and manage uncertainty for fuzzifier m. Thong and Son proposed picture fuzzy clustering based on the picture fuzzy set (PFS) in [10]. Second, the kernel-based method is applied to improve the fuzzy clustering quality.…”

“…Thong and Son did significant work on clustering based on PFS. In [10], a picture fuzzy clustering algorithm, called FC-PFS, was proposed. In order to determine the number of clusters, they built an automatically determined most suitable number of clusters based on particle swarm optimization and picture composite cardinality for a dataset [23].…”

“…They also extended the picture fuzzy clustering algorithm for complex data [24]. Unlike the method in [10], Son presented a novel distributed picture fuzzy clustering method on the picture fuzzy set [25]. We can note that the basic ideas of the fuzzy set, the intuitionistic fuzzy set and the SVNS are consistent in the data clustering, but there are differences in the representation of the objects, so that the clustering objective functions are different.…”

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

“…Based on the fuzzy set, several additional and hybrid concepts such as theintervalvalued fuzzy set [69], the type-2 fuzzy set [69], the intuitionistic fuzzy set [2] were developed. Fuzzy sets play a tremendous role in signal processing [25], control theory [14], reasoning [7], decision making [23], medical diagnosis [31], geo-demographic analysis [33,37,41,42,65], dental segmentation [47,48,59], compression [43], recommender systems [34,36,38] and other fields [8,10,35,39,40,46,49,50,[56][57][58].…”