2. DEFINITION
A set defined using a characteristic function that
assigns a value of either 0 or 1 to each element of
the universe, thereby discriminating between
members and non-members of the crisp set under
consideration. In the context of fuzzy sets theory,
we often refer to crisp sets as “classical” or
“ordinary” sets.
3. EXAMPLE
In a crisp set, an element is either a member of
the set or not. For example, a jelly bean belongs
in the class of food known as candy. Mashed
potatoes do not. Fuzzy sets, on the other hand,
allow elements to be partially in a set.
4.
5.
6. VENN DIAGRAM
A diagram representing mathematical or logical sets pictorially
as circles or closed curves within an enclosing rectangle (the
universal set), common elements of the sets being represented
by intersections of the circles.
7. MEMBERSHIP
The state or status of being a member. The symbol
indicates set membership and means “is an
element of” so that the statement x ∈ A means that
is an element of the set . In other words, is one of
the objects in the collection of (possibly many)
objects in the set .
For example, if A is the set {♢,♡,♣,♠},
then ♡∈A but △∉A (where the symbol ∉ means “not
an element of”). Or if I is the interval [1,2], then x
∈I means x is some real number in that interval,
i.e., x satisfies 1≤x≤2.
8.
9. FAMILY OF SETS
In set theory and related branches of mathematics, a collection F
of subsets of a given set S is called a family of subsets of S, or
a family of sets over S. More generally, a collection of
any sets whatsoever is called a family of sets.
15. OPERATIONS : UNION
The union of two sets A and B is a set containing the
elements of both set A and set B. It is represented as (A
∪ B)
As you may already know, Crisp Sets consists of well-defined
collection of objects. Well-defined in the sense that the
objects either belong to or doesn’t belong to a set. Here are
some of the most important operations of Crisp sets:
16. INTERSECTION
In mathematics, the intersection A ∩ B of two
sets A and B is the set that contains
all elements of A that also belong to B (or
equivalently, all elements of B that also belong
to A), but no other elements.
17. DIFFERENCE
When all sets under consideration are considered to be subsets of
a given set U, the absolute complement of A is the set of
elements in U but not in A. The relative complement of A with
respect to a set B, also termed the difference of sets A and B,
written B ∖ A, is the set of elements in B but not in A.
18. COMPLEMENT
When all sets under consideration are considered to be subsets of a
given set U, the absolute complement of A is the set of elements
in U but not in A. The relative complement of A with respect to a
set B, also termed the difference of sets A and B, written B ∖ A, is
the set of elements in B but not in A.
