An interval-valued matrix factorization based trust-aware collaborative filtering algorithm for recommendation systems

In existing trust-aware collaborative filtering algorithms, each trust relationship between two users is usually represented by a real number, but such a number is neither sufficient to reflect the quantity of the trust relationship existing in the user's mind nor easy to be given. This leads to the inaccuracy of the trust relationship and poor final recommendations. To solve this problem, we propose an approach to deduce interval-valued trust relationships from the given real-valued trust relationships, which enables the new trust relationships to optimally reflect the true trust relationships existing in users' minds. The coming problem we face is how to fuse the interval- valued trust relationships and the real-valued ratings. Though most existing trust-aware collaborative filtering algorithms use matrix factorization to fuse the real-valued data, they are not capable of fusing interval-valued trust relationships and real-valued ratings. The reason is that the arithmetic operations on intervals and arithmetic operations on real numbers are different. Therefore, we proposed a novel interval-valued matrix factorization approach. After that, an interval-valued matrix factorization based trust-aware collaborative filtering (IMF_TCF) algorithm is designed. The experiments carried out with open datasets indicate that IMF_TCF achieves the best recommendation performance compared with the state-of-the-art algorithms.