This article addresses the robust dissipativity and passivity problems for a class of Markovian switching complex-valued neural networks with probabilistic time-varying delay and parameter uncertainties. The main objective of this article is to study the proposed problem from a new perspective, in which the relevant transition rate information is partially unknown and the considered delay is characterized by a series of random variables obeying bernoulli distribution. Moreover, the involved parameter uncertainties are considered to be mode-dependent and norm-bounded. Utilizing the generalized It $\hat{o}$'s formula under the complex version, the stochastic analysis techniques and the robust analysis approach, the $(M,N,W)$-dissipativity and passivity are ensured by means of complex matrix inequalities, which are mode-delay-dependent. Finally, two simulation examples are provided to verify the effectiveness of the proposed results.