Clustering of Triangular Fuzzy Data based on Heuristic Methods

In this paper, a new version of the particle swarm optimization (PSO) algorithm using a linear ranking function is proposed for clustering uncertain data. In the proposed Uncertain Particle Swarm Clustering method, called UPSC method, triangular fuzzy numbers (TFNs) are used to represent uncertain data. Triangular fuzzy numbers are a good type of fuzzy numbers and have many applications in the real world. In the UPSC method input data are fuzzy numbers. Therefore, to upgrade the standard version of PSO, calculating the distance between the fuzzy numbers is necessary. For this purpose, a linear ranking function is applied in the fitness function of the PSO algorithm to describe the distance between fuzzy vectors. The performance of the UPSC is tested on six artificial and nine benchmark datasets. The features of these datasets are represented by TFNs. The experimental results on fuzzy artificial datasets show that the proposed clustering method (UPSC) can cluster fuzzy datasets like or superior to other standard uncertain data clustering methods such as Uncertain K-Means Clustering (UK-means) and Uncertain K-Medoids Clustering (UK-medoids) algorithms. Also, the experimental results on fuzzy benchmark datasets demonstrate that in all datasets except Libras, the UPSC method provides better results in accuracy when compared to other methods. For example, in iris data, the clustering accuracy has increased by 2.67% compared to the UK-means method. In the case of wine data, the accuracy increased with the UPSC method is 1.69%. As another example, it can be said that the increase in accuracy for abalone data was 4%. Comparing the results with the rand index (RI) also shows the superiority of the proposed clustering method.