  Neutrosophic Over-/Under-/Off-Set and -Logic were defined by the author in
1995 and published for the first time in 2007. We extended the neutrosophic set
respectively to Neutrosophic Overset {when some neutrosophic component is over
1}, Neutrosophic Underset {when some neutrosophic component is below 0}, and to
Neutrosophic Offset {when some neutrosophic components are off the interval [0,
1], i.e. some neutrosophic component over 1 and other neutrosophic component
below 0}. This is no surprise with respect to the classical fuzzy set/logic,
intuitionistic fuzzy set/logic, or classical/imprecise probability, where the
values are not allowed outside the interval [0, 1], since our real-world has
numerous examples and applications of over-/under-/off-neutrosophic components.
For example, person working overtime deserves a membership degree over 1, while
a person producing more damage than benefit to a company deserves a membership
below 0. Then, similarly, the Neutrosophic Logic/Measure/Probability/Statistics
etc. were extended to respectively Neutrosophic Over-/Under-/Off-Logic,
-Measure, -Probability, -Statistics etc. [Smarandache, 2007].
