3) Neutrosophic Crisp Set
with Type III if it satisfies [A.sub.1] [intersection] [A.sub.2] [intersection] [A.sub.3] = [phi] and [A.sub.1] [union] [A.sub.2] [union] [A.sub.3] = X (NCS-Type III for short).
Analogously, we know when P is a crisp set
, that is, [[PSI].sub.P] (x) = 0, [[DELTA].sub.P] (x) = 1 for all x [member of] X, DE(A, P) can measure the uncertain information of IvIFS, including fuzziness and intuitionism.
where d(u([alpha]), u) is the distance between crisp set
u([alpha]) and fuzzy set u.
Before discussing the analysis and interpretation associated with Table 1, an introduction to the basic concepts of the crisp set
and Boolean algebra method will be presented.
A fuzzy set A is defined in the crisp set
U as a set of ordered pairs A = <(w,[[mu].sub.A](w))|w [member of]U>, where [[mu].sub.A] (w) is the membership function, which indicates the degree that w belongs to A [12-15].
The crisp set
[A.sub.[alpha]] of elements of X that belong to the fuzzy set A at least to the degree [alpha] is called the [alpha]-cut of the fuzzy set A:
Salama et al [23,24] put some Ibasic concepts of the neutrosophic crisp set
, and their operations, and because of their wide applications and their grate flexibility to solve the problem!, we used these concepts to define new types of neutrosophic points, that, we called neutrosophic crisp points [[NCP.sub.N]].
Results show that the conclusion about the nonemptiness for the crisp set
[M.sub.C](S, R) can be extended to the corresponding fuzzy set, but not for the crisp set
The Characteristic function [[mu].sub.A] of a crisp set
A [subset or equal to] X assigns a value either 0 or 1 to each member in X.
The race was run on March 31 and from the off Crisp set
a fast pace.
When Stuart Crisp set
up The Fun Centre in Caernarfon almost three years ago he made sure all the play equipment was strong enough to take the weight of adults.
Alblowi  introduced the notions of neutrosophic crisp set
and neutrosophic crisp topological space.