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

Neutrosophic Sets and Systems 12:3-8 (2016)
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Abstract

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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Florentin Smarandache
University of New Mexico