Visual cryptography (VC) is a variant form of secret sharing. In general threshold setting, the k-out-of-n VC allows that, in a set of n participants, any k can recover and reconstruct the secret by stacking their shares. Recently, the notion of multiple-secret VC has been introduced to embed multiple secrets. Region incrementing visual cryptography (RIVC) is referred to as a new type of multi-secret VC. RIVC defines s layers and takes s secrets, and then embeds each secret into each layer. The layers are defined by the number of participants; for example, let two secrets and two layers be S-2, S-3 and L-2, L-3 in two-out-of-three RIVC, where any two participants in L-2 can recover S-2 and three in L-3 can recover S-2, S-3. However, there is another multi-secret VC, called fully incrementing visual cryptography (FIVC), which also has the layers, but only one secret S-i will reveal in one layer L-i. In this paper, our stating point is to propose a new notion of non-monotonic visual cryptography (NVC) for human vision system as a primitive to construct FIVC. We first present an ideal construction of simple NVC, which relies on a slightly unreasonable assumption. Based on the simple NVC, we show a few methods to extend the functionality for complicated cases of NVC. Then, the generic construction is presented as a systematic manner to eliminate the above-mentioned assumption. Finally, we formally introduce a transformation NVC-to-FIVC algorithm, which takes NVC as input and then produce a construction of FIVC. Also, show a demonstration the NVC-to-RIVC algorithm, and analyze some properties regarding NVC. We believe that the notion of NVC can potentially find other applications and is of independent interest.