Florentin Smarandache
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. Smarandache extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, Neutrosophic Underset {when some neutrosophic component is 1 and other neutrosophic component 1 and < 0 are real in our world, so we have to take them into consideration. Then, similarly, the Neutrosophic Logic / Measure / Probability / Statistics etc. were extended to respectively Neutrosophic Over- / Under- / Off -Logic, -Measure, -Probability, -Statistics etc. Many practical obvious examples are presented in this book, in order to show that in our everyday life we continuously deal with neutrosophic over-/under-/off- theory and applications.
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