Artificial Intelligence for Big Data

Attributes and notations of crisp sets

A crisp set is a collection of entities that can be clearly separated as members versus non-members, for example, a set of living objects versus non-living objects. In this case, the container fully includes or fully excludes the elements. There are several ways in which crisp sets can be defined:

• A set of even numbers greater than 0 and less than 10
  • A = {2,4,6,8}
• A set of elements that belong to another set, P and Q
  • A = {x | x is an element belonging to P and Q}

• µ_A(X)= 1 if ( x ∈ A), 0 if (x ∉ A) 
• Φ: Represents a null or empty set
• Power set P(A) = {X | x ⊆ A}: This is a set containing all the possible subsets of A
• For the crisp sets A and B containing a super-set of elements within X: 
  • x ⊂ ...