The proposed article mainly comprises of ideas and motivations that led to the generalisation of the usual or the crisp sets. Moving forward we intend to look into how the definitions were modifed to suit the meaning of the existing definitions and establish link between them, that is to say that we, after giving formal definitions of the aforementioned sets and norms on these new sets would draw parallel between them and the usual sets and the norm. We will then study some riveting topological and algebraic properties of the same.