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In this paper, we present a fusion rule for distributed multihypothesis decision systems where communication patterns among sensors are given and the fusion center may also observe data. It is a specific form of the most general fusion rule, independent of statistical characteristics of observations and decision criteria, and thus, is called a unified fusion rule of the decision system. To achieve globally optimum performance, only sensor rules need to be optimized under the proposed fusion rule for the given conditional distributions of observations and decision criterion. Following this idea, we present a systematic and efficient scheme for generating optimum sensor rules and hence, optimum fusion rules, which reduce computation tremendously as compared with the commonly used exhaustive search. Numerical examples are given, which support the above results and provide a guideline on how to assign sensors to nodes in a signal detection networks with a given communication pattern. In addition, performance of parallel and tandem networks is compared.