Trust systems represent a significant trend in decision support for social networks' service provision. The basic idea is to allow users to rate each other even without being direct neighbours. In this case, the purpose is to derive a trust score for a given user, which could be of help to decide whether to trust other users or not. In this article, we investigate the properties of trust propagation within social networks, based on the notion of transitivity, and we introduce the TISoN model to generate and evaluate Trust Inference within online Social Networks. To do so, (i) we develop a novel TPS algorithm for Trust Path Searching where we define neighbours' priority based on their direct trust degrees, and then select trusted paths while controlling the path length; and, (ii) we develop different TIM algorithms for Trust Inference Measuring and build a trust network. In addition, we analyse existing algorithms and we demonstrate that our proposed model better computes transitive trust values than do the existing models. We conduct extensive experiments on a real online social network dataset, Advogato. Experimental results show that our work is scalable and generates better results than do the pioneering approaches of the literature