We study decision fusion for decentralized detection in a wireless sensor network. Motivated by the sub-optimality of previously proposed fusion rules, we investigate a new set of rules, termed 'generalized nonlinearities'. Our approach seeks to preserve the optimality of the likelihood ratio (LR) test, without requiring a priori information about the channel statistics or the local sensor performance indices. We derive such rules for coherent and noncoherent detection. Performance evaluation reveals notable advantages of the proposed rules relative to existing ones. Under coherent detection, it is shown that the proposed technique outperforms the LR rule under channel mismatch (an indication of its robustness). For noncoherent detection, we apply the Central Limit Theorem in conjunction with generalized nonlinearities technique to provide insights not readily available under the LR rule.