Book excerpt: In this paper, we first propose the concept of Vague-valued possibility Neutrosophic vague soft expert sets (VPNVSEsets in short). It is a combination of vague-valued possibility neutrosophic vague sets and soft expert sets. We also define its basic operations and study some related properties. Lastly an algorithm is proposed applied to the concept of vague-valued possibility Neutrosophic vague soft expert sets in hypothetical decision making problem. Here we associate the degree of belongingness degree of indeterminacy and non-belongingness of the elements of universe set with the vague –valued possibility set.