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Trust issue is presently a research hotspot in military information grid. This paper first proposes a SOA-based unified identity authentication scheme, which can transplant the existing account systems into the new one by means of account association, to solve the problem of inter-network identity authentication. Then, this paper develops an asymmetric trust model based on fuzzy logic. This model takes into account several factors which may affect trust evaluation in military information grid, such as non-symmetric trust relationship between networks, time self-decay. Thus, the model will be more practical and effective.