A new similarity measure between picture fuzzy sets with applications to pattern recognition and clustering problems

In this paper, similarity measures have been discussed which has the potential to discriminate analogous but contrary picture fuzzy sets (PFSs). We have also described their properties along with their implementation in pattern recognition by taking numerical examples. To implement the application of similarity measures in real life problems, we have taken real data from the repository of machine learning. Next, the real data set has been transformed into picture fuzzy (PF)- environment. Thereafter, by using the idea of degree of confidence (DOC), we have compared the proposed measures with existing measures and the potential of proposed measures have been discussed. Furthermore, by extending the idea of maximum spanning tree (MST) and clustering algorithm, a picture fuzzy maximum spanning tree clustering method has been proposed. Although, existing PF-clustering methods can also give reasonable results but proposed method is simple and having less computational cost. Additionally, we have compared the proposed measures with existing PF-similarity measures in terms of linguistic hedges. Proposed measures meet all the conditions as compared to existing measures from linguistic hedges point of view. Thus, comparative results of pattern recognition problems, DOC and linguistic hedges shows the superiority of proposed measures over existing measures.