# Crisp Sets

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## Crisp Sets

The fuzzy set term for traditional set theory. That is, an object either belongs to a set, or does not.

## Crisp Set

A term for a mathematical model that does not use fuzzy logic. Fuzzy logic is a mathematical or computer program that attempts to approximate the ambiguity inherent to human reasoning. Thus, a crisp set is any program that organizes data into neat categories where each data point can belong to one, and only one, category.
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Al-Omeri, Neutrosophic crisp Sets via Neutrosophic crisp Topological Spaces NCTS, Neutrosophic Sets and Systems, Vol.13, 2016, pp.96-104
(1) a crisp set is always nonfuzzy; i.e., an IVIFS has no vagueness when it degenerates to a crisp set;
Effectively, an [alpha]-cut is a means to defuzzify a fuzzy set into a crisp set at desired [alpha]-levels which reflect the perceived risk.
Neutrosophic crisp sets with three types are neutrosophic crisp set.
Due to the problems that the article was in relation to crisp sets, to overcome these problems, crisp data should be defined as a fuzzy, so as not to lose any data.
In the case of step fuzzy set, we have fixed the number of [alpha]-cut sets, so it is easy to transform a fuzzy set into a series of crisp sets. But there may be a large number of [alpha]-cut sets, which are not necessary in calculating Seiner point of a fuzzy set.
Observe that in the case of crisp set, the membership function can only takes the extreme values of the interval [0,1].
Therefore, 0 [less than or equal to] [alpha]D [less than or equal to] 1, if [alpha]D(X) = 1, X it is a definable set regarding the attributes B, that is, X is crisp set. If [alpha]D(X) < 1, X is rough set regarding the attributes D.
The research case scenario illustrates how one can use crisp sets and Boolean algebra to examine different combinations of conditions associated with cases.
Uncertain information means the information about an object in the shape of crisp sets (intervals).
The company has developed a reputation for crisp sets, colourful costumes and challenging choreography setting a standard for touring classical dance with the exceptionally high quality of its productions and dancers.
Although no one would deny them the crisp sets, character-defining costumes and clarifying lighting that give their plays a thoroughly professional look, the directors and dramaturgs have been a bit too kind.

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