Decision-making in machine learning using novel picture fuzzy divergence measure

Some tools such as entropy, divergence measures and similarity measures are applied to real-world phenomena like decision-making, robotics, pattern recognition, clustering, expert and knowledge-based system and medical diagnosis. An intuitionistic fuzzy set (IFS) comprises of membership function and non-membership function, but neutrality function is missing in IFS. Therefore, picture fuzzy set (PFS) is an excellent tool to handle such situations when there are answers like yes, no, abstain and refusal. PFS is the generalization of fuzzy set (FS) and intuitionistic fuzzy set (IFS) and shows better adaptation to various real-world problems. To draw conclusions for these problems, based on discrimination between two probability distributions, tools such as divergence measure play a crucial role. The aim of this study is to propose a divergence measure for picture fuzzy sets with its validity proof and to deliberate its key properties. Besides, the newly developed divergence measure is applied to decision-making in machine learning such as pattern recognition, medical diagnosis and clustering using numerical illustrations. To validate the proposed method and to check its effectiveness, expediency and legitimacy, a comparative analysis is given and also the superiority of the divergence measure is tested over the existing methods by comparing their results.