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Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset

Autori: Florentin Smarandache

Editorial: 2016.


Neutrosophic Over–/Under-/Off-Set and -Logic were defined for the first time by the author in 1995 and presented to various international and national conferences and seminars between 1995-2016 and first time published in 2007. They are totally different from other sets/logics/probabilities/statistics. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 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.