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Furthermore, throughout the paper, the set of all closed subintervals of [0,1] is denoted by [I], the domain or universe of discourse is denoted by a set X = {[x.sub.1], [x.sub.2], ..., [x.sub.n]], the collection of all the crisp sets is denoted by P(X), and the set of all IVIFSs in X are denoted by IVIF(X).
2) Neutrosophic Crisp Set with Type II if it satisfies [A.sub.1] [intersection] [A.sub.2] = [phi], [A.sub.1] [intersection] [A.sub.3] = [phi] and [A.sub.2] [intersection] [A.sub.3] = [phi] and [A.sub.1] [union] [A.sub.2] [union] [A.sub.3] = X (NCS-Type II for short).
(a) E(A) = 0 iff A is a crisp set; that is, [[mu].sub.A] (x) = [1,1], [v.sub.A] (x) = [0, 0] or [[mu].sub.A] (x) = [0, 0], [v.sub.A] (x) = [1,1] for all x [member of] X;
Then one calls u([[alpha].sub.0]) the optimal approximate crisp set to u if
Fuzzy sets are an extension of the classic notion of sets (Bourbaki, 1968) called, for sake of understanding, crisp sets. A set A of the latter type can be defined, in terms of the membership function, as
Also process the incomplete data is based on the lower and upper approximations and theory was defined as a pair of the two crisp sets to the approximations.
71 Before introducing the basic concepts of the crisp set and Boolean algebra method, a hypothetical research scenario focusing on a student affairs research interest will be presented.
The band earned its devotion with a crisp set culled from new songs and classics, each tune a smart, provocative invitation to agree with Bad Religion that the status quo is evil and soul-crushing.
In the case of probabilistic information, a crisp set of events or values is given and the probabilistic measure in that is set.
As England's public upheavals of the mid-seventeenth century were turning ominous, the antinomian preacher Tobias Crisp set his own stamp upon tempestuous times.
A fuzzy set differs from a classical set (referred to as a crisp set hereafter) in that the characteristic function can take any value in the interval [0,1].
Former Aston Villa youngster Richard Crisp set up Evran Wright for his 19th goal of the season to raise Halsowen's promotion hopes after only eight minutes, but the visitors drew level through Andy Pincher just before halime.