Degrees of Membership > 1 and < 0 of the Elements With Respect to a Neutrosophic OffSet


  • Florentin Smarandache Mathematics & Science Department, University of New Mexico 705 Gurley Ave., Gallup, NM 87301, USA


Neutrosophic overset, neutrosophic underset, neutrosophic offset, neutrosophic overlogic, neutrosophic underlogic, neutrosophic offlogic, neutrosophic overprobability, neutrosophic underprobability, neutrosophic offprobability, overmembership (membership degree > 1), undermembership (membership degree < 0), offmembership (membership degree off the interval [0, 1]


We have defined the Neutrosophic Over- /Under-/Off-Set and -Logic for the first time in 1995 and published in 2007. During 1995-2016 we presented them to various national and international conferences and seminars ([16]-[37]) and did more publishing during 2007-2016 ([1]-[15]). These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, to 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 since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components.


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How to Cite

Smarandache, F. . (2016). Degrees of Membership > 1 and < 0 of the Elements With Respect to a Neutrosophic OffSet. Neutrosophic Sets and Systems, 12, 3-8. Retrieved from