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

Therefore, the neutrosophic logic, neutrosophic set,

neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus, and so forth were born in neutrosophy [15].

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.