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Trustworthiness of IT systems can be justified using the concept of a trust case. A trust case is an argument structure which encompasses justification and evidence supporting claimed properties of a system. It represents explicitly an expert's way of assessing that a certain object has certain properties. Trust cases can be developed collaboratively on the basis of evidence and justification of varying quality. They can be complex structures impossible to comprehend fully by a non-expert. A postulated model of communicating trust case contents to an 'ordinary' user is an expert acting on user's behalf and communicating his/her assessment to the user. Therefore, a mechanism for issuing and aggregating experts' assessments is required. The paper proposes such a mechanism which enables assessors to appraise strength of arguments included in a trust case. The mechanism uses Dempster-Shafer's model of beliefs to deal with uncertainty resulting from the lack of knowledge of the expert. Different types of argumentation strategies were identified and for each of them appropriate combination rules were presented.