Research on K-medoids Algorithm with Probabilistic-based Expressions and Its Applications

Nowadays, the decision environment is becoming more and more complicated due to the development of society and science, and people receiving different types of information every day and gradually form their unique cognitions and knowledge backgrounds. In this situation, people tend to provide their preferences or evaluations through multiple information expression formats, such as the probabilistic hesitant fuzzy sets, the probabilistic linguistic term sets and the probabilistic interval preference ordering sets. In this paper, we deeply investigate the relationships among these three probabilistic-based expressions and introduce two transformation functions for them in order to make the information formats unified. Besides, for the probabilistic hesitant fuzzy sets, three novel distance measures are proposed, i.e., the minimal distance, the central distance, and the improved distance, which are useful tools to measure the difference between the probabilistic hesitant fuzzy elements. In order to fuse the different formats of information and get valuable results from it, the K-medoids algorithm for the probabilistic-based expressions is developed. The algorithm is applied to classify the merchants on the website of Dianping.com, so that the results can be provided to customers to help them make decisions.