The distance of probabilistic fuzzy sets for classification

• We propose the concept of the distance between probabilistic fuzzy sets.
• The corresponding proofs of the proposed distance measure are conducted.
• We propose PFS-based distance classifier.
• The PFS-based distance classifier is applied to classification problems.

The probabilistic fuzzy set (PFS) is designed for handling the uncertainties with both stochastic and fuzzy nature. In this paper, the concept of the distance between probabilistic fuzzy sets is introduced and its metric definition is conducted, which may be finite or continuous. And some related distances are discussed. The proposed distance considers the random perturbation in progress by introducing the distance of probability distribution, thus it improves the ability to handle random uncertainties, and some inadequacy of the distance of probability distribution is remedied. Finally, a PFS-based distance classifier is proposed to discuss the classification problem, the numerical experiment shows the superiority of this proposed distance in fuzzy and stochastic circumstance.