Neutrosophy, Neutrosophic Set,
Neutrosophic Probability (third edition), American Research Press: Rehoboth, NM, USA, 1999.
[4.] Smarandache, F.: Neutrosophy,
Neutrosophic Probability, Sets and Logic, Proquest Information & Learning, Ann Arbor, Michigan, USA, 105p,1998
Also, he suggested an extension of the classical probability and imprecise probability to "
neutrosophic probability".
Neutrosophy is the basis of neutrosophic logic,
neutrosophic probability, neutrosophic set, and neutrosophic statistics.
A cloud is a neutrosophic set, because its borders are ambiguous, and each element (water drop) belongs with a
neutrosophic probability to the set (e.g.
One uses the definitions of
Neutrosophic probability and Neutrosophic set operations.
Further the Smarandache
neutrosophic probability bivector will be a bicolumn vector which can take entries from [-1, 1] [union] [-I, I] whose sum can lie in the biinterval [-1, 1] [union] [-I, I].
Neutrosophy:
neutrosophic probability, set and logic, American Research Press, Rehoboth, (1998).
Let X be a non- empty set and Abe any type of neutrosophic crisp set on a space X, then the
neutrosophic probability is a mapping NP: X [right arrow] [[0,1].sup.3], NP(A) = <{P([A.sub.1]),P([A.sub.2]),P([A.sub.3])>, that is the probability of a neutrosophic crisp set that has the properly that--
Similar generalizations are done for n-Valued Refined Neutrosophic Set, and respectively n-Valued Refined
Neutrosophic Probability.
He demonstrated that the
neutrosophic probability of the true price of the derivative security being given by any theoretical pricing model is obtainable as NP (H [intersection] [M.sup.C]); where NP stands for
neutrosophic probability, H = {p : p is the true price determined by the theoretical pricing model }, M = {p : p is the true option price determined by the prevailing market price } and the C superscript is the complement operator.