Picture Fuzzy Soft Matrices and Application of Their Distance Measures to Supervised Learning: Picture Fuzzy Soft k-Nearest Neighbor (PFS-kNN)

Abstract

This paper redefines picture fuzzy soft matrices (pfs-matrices) because of some of their inconsistencies resulting from Cuong’s definition of picture fuzzy sets. Then, it introduces several distance measures of pfs-matrices. Afterward, this paper proposes a new kNN-based classifier, namely the Picture Fuzzy Soft k-Nearest Neighbor (PFS-kNN) classifier. The proposed classifier utilizes the Minkowski’s metric of pfs-matrices to find the k-nearest neighbor. Thereafter, it performs an experimental study utilizing four UCI medical datasets and compares to the suggested approach using the state-of-the-art kNN-based classifiers. To evaluate the performance of the classification, it conducts ten iterations of five-fold cross-validation on all the classifiers. The findings indicate that PFS-kNN surpasses the state-of-the-art kNN-based algorithms in 72 out of 128 performance results based on accuracy, precision, recall, and F1-score. More specifically, the proposed method achieves higher accuracy and F1-score results compared to the other classifiers. Simulation results show that pfs-matrices and PFS-kNN are capable of modeling uncertainty and real-world problems. Finally, the applications of pfs-matrices to supervised learning are discussed for further research.