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

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 and did more publishing during 2007-2016. 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 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.

Keywords

• Neutrosophic overset
• neutrosophic underset
• neutrosophic offset
• neutrosophic overlogic
• neutrosophic underlogic
• neutrosophic offlogic
• neutrosophic overprobability
• neutrosophic underprobability
• neutrosophic offprobability