Open computational systems, such as e-business, peer-to-peer networks and grid, are becoming the main trends. Open computational systems are characterized as both open and dynamic. The interacting parties may be strange and selfish members, which brings great risks to the interactions. The traditional secure mechanisms depend mainly on the authority center which is difficult to establish in open computational systems, so it is no longer sufficient for the open computational systems. Trust management inspired by the trust mechanisms in society is an important research of social computing. Trust management is trying to build up similar trust mechanisms in open computational systems, which is considered a promising way to solve the trust problem in open computational systems.From the point of view of trust representation, this dissertation researched trust management based on DSmT, including trust representation, acquisition, transitivity, accumulation, decision, malicious behavior resistance, second-hand trust evaluation modification and application to recommender systems. This study mainly has four contributes:(1) DSmTrust, a trust model based on DSmT, is provided in order to handle the common problem of insufficient trust representation in open computational systems. Besides DSmTrust, further problems including trust acquirement, trust decision and malicious behavior resistance are studied. Simulations show the efficiency and effectiveness by comparisons.(2) The DSmT Subjective Logic which is an extension of the Subjective Logic is presented. The discounting operator and consensus operator are applied to trust transitivity and trust accumulation of DSmTrust, respectively. The flexibility of discounting operator and the rationality of consensus operator are proved by experiments and examples.(3) A disturbing model is presented to modify the second-hand trust evaluations because of the problem of inaccurate second-hand information in trust management. This disturbing model is reduced to the inverse problem of DSmT. The simulations indicate that the disturbing model can explain and modify well the difference between the second-hand trust evaluations and the first-hand trust evaluations.(4) DSmTrust is preliminarily applied to recommender systems. The constraint of common ratings in collaborative filtering is relieved in DSmTrust by trust transitivity. The preliminary results show that DSmTrust can effectively handle the sparse problem and cold start problem comparing with traditional collaborative filtering, and the recommendation precision of DSmTrust is better than Massa’s approach.This dissertation applies DSmT to trust management. On the one hand, this work provides a novel approach to represent and handle trust for the field of trust management and it can be a support of the future interoperable trust model for the heterogeneous trust models. On the other hand, this study which is a paradigm for the application of DSmT will drive the development of DSmT.